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Автор: Grafiati

Опубліковано: 14 березня 2023

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1

Martelli, Bruno. "Complexity of PL manifolds." Algebraic & Geometric Topology 10, no. 2 (May 23, 2010): 1107–64. http://dx.doi.org/10.2140/agt.2010.10.1107.

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2

Ayala, R., A. Quintero, and W. J. R. Mitchell. "Triangulating and recognising PL homology manifolds." Mathematical Proceedings of the Cambridge Philosophical Society 104, no. 3 (November 1988): 497–504. http://dx.doi.org/10.1017/s0305004100065683.

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3

Gu, David Xianfeng, and Emil Saucan. "Metric Ricci Curvature for PL Manifolds." Geometry 2013 (November 20, 2013): 1–12. http://dx.doi.org/10.1155/2013/694169.

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Анотація:

We introduce a metric notion of Ricci curvature for PL manifolds and study its convergence properties. We also prove a fitting version of the Bonnet-Myers theorem, for surfaces as well as for a large class of higher dimensional manifolds.

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4

Jaco, William, and J. Hyam Rubinstein. "PL minimal surfaces in 3-manifolds." Journal of Differential Geometry 27, no. 3 (1988): 493–524. http://dx.doi.org/10.4310/jdg/1214442006.

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5

Casali, M. R., and P. Cristofori. "Coloured graphs representing PL 4-manifolds." Electronic Notes in Discrete Mathematics 40 (May 2013): 83–87. http://dx.doi.org/10.1016/j.endm.2013.05.016.

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6

Casali, M. R., P. Cristofori, and C. Gagliardi. "PL 4-manifolds admitting simple crystallizations: framed links and regular genus." Journal of Knot Theory and Its Ramifications 25, no. 01 (January 2016): 1650005. http://dx.doi.org/10.1142/s021821651650005x.

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Анотація:

Simple crystallizations are edge-colored graphs representing piecewise linear (PL) 4-manifolds with the property that the 1-skeleton of the associated triangulation equals the 1-skeleton of a 4-simplex. In this paper, we prove that any (simply-connected) PL 4-manifold [Formula: see text] admitting a simple crystallization admits a special handlebody decomposition, too; equivalently, [Formula: see text] may be represented by a framed link yielding [Formula: see text], with exactly [Formula: see text] components ([Formula: see text] being the second Betti number of [Formula: see text]). As a consequence, the regular genus of [Formula: see text] is proved to be the double of [Formula: see text]. Moreover, the characterization of any such PL 4-manifold by [Formula: see text], where [Formula: see text] is the gem-complexity of [Formula: see text] (i.e. the non-negative number [Formula: see text], [Formula: see text] being the minimum order of a crystallization of [Formula: see text]), implies that both PL invariants gem-complexity and regular genus turn out to be additive within the class of all PL 4-manifolds admitting simple crystallizations (in particular, within the class of all “standard” simply-connected PL 4-manifolds).

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7

Casali, Maria Rita. "Classifying Pl 5-Manifolds by Regular Genus: The Boundary Case." Canadian Journal of Mathematics 49, no. 2 (April 1, 1997): 193–211. http://dx.doi.org/10.4153/cjm-1997-010-3.

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AbstractIn the present paper, we face the problem of classifying classes of orientable PL 5-manifolds M5 with h ≥ 1 boundary components, by making use of a combinatorial invariant called regular genusG(M5). In particular, a complete classification up to regular genus five is obtained: where denotes the regular genus of the boundary ∂M5 and denotes the connected sumof h ≥ 1 orientable 5-dimensional handlebodies 𝕐αi of genus αi ≥ 0 (i = 1, . . . ,h), so that .Moreover, we give the following characterizations of orientable PL 5-manifolds M5 with boundary satisfying particular conditions related to the “gap” between G(M5) and either G(∂M5) or the rank of their fundamental group rk(π1(M5)): Further, the paper explains how the above results (together with other known properties of regular genus of PL manifolds) may lead to a combinatorial approach to 3-dimensional Poincaré Conjecture.

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8

Jeoung, Chang-Sik, and Yong-Kuk Kim. "PL FIBRATORS AMONG PRODUCTS OF HOPFIAN MANIFOLDS." Bulletin of the Korean Mathematical Society 43, no. 4 (November 30, 2006): 841–46. http://dx.doi.org/10.4134/bkms.2006.43.4.841.

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9

Kim, Yong-Kuk. "THE PL FIBRATORS AMONG GEOMETRIC 4-MANIFOLDS." Communications of the Korean Mathematical Society 19, no. 2 (April 1, 2004): 337–43. http://dx.doi.org/10.4134/ckms.2004.19.2.337.

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10

Daverman, Robert J., Young Ho Im, and Yongkuk Kim. "PL fibrator properties of partially aspherical manifolds." Topology and its Applications 140, no. 2-3 (May 2004): 181–95. http://dx.doi.org/10.1016/j.topol.2003.07.016.

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11

Basak, Biplab. "Genus-minimal crystallizations of PL 4-manifolds." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 59, no. 1 (February 23, 2017): 101–11. http://dx.doi.org/10.1007/s13366-017-0334-x.

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12

Cavicchioli, Alberto, Friedrich Hegenbarth, and Dušan Repovš. "On the stable classification of certain 4-manifolds." Bulletin of the Australian Mathematical Society 52, no. 3 (December 1995): 385–98. http://dx.doi.org/10.1017/s000497270001488x.

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Анотація:

We study the s-cobordism type of closed orientable (smooth or PL) 4–manifolds with free or surface fundamental groups. We prove stable classification theorems for these classes of manifolds by using surgery theory.

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13

Saucan, Emil. "Metric Ricci Curvature and Flow for PL Manifolds." Actes des rencontres du CIRM 3, no. 1 (2013): 119–29. http://dx.doi.org/10.5802/acirm.61.

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14

Daverman, Robert J. "The PL fibrators among aspherical geometric $3$-manifolds." Michigan Mathematical Journal 41, no. 3 (1994): 571–85. http://dx.doi.org/10.1307/mmj/1029005081.

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15

Jingmei, Guo. "PL embeddings ofPL manifolds into some Euclidean spaces." Acta Mathematica Sinica 5, no. 1 (March 1989): 27–36. http://dx.doi.org/10.1007/bf02107620.

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16

Costa, Antonio F., and Luigi Grasselli. "Universal coverings of PL-manifolds via coloured graphs." Aequationes Mathematicae 44, no. 1 (August 1992): 60–71. http://dx.doi.org/10.1007/bf01834205.

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17

McClure, J. E. "On the chain-level intersection pairing for PL manifolds." Geometry & Topology 10, no. 3 (October 4, 2006): 1391–424. http://dx.doi.org/10.2140/gt.2006.10.1391.

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18

Casali, Maria Rita, and Carlo Gagliardi. "Classifying PL 5-Manifolds Up to Regular Genus Seven." Proceedings of the American Mathematical Society 120, no. 1 (January 1994): 275. http://dx.doi.org/10.2307/2160196.

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19

Im, Young-Ho. "SOME MANIFOLDS WITH NONZERO EULER CHARACTERISTIC AS PL FIBRATORS." Honam Mathematical Journal 29, no. 3 (September 25, 2007): 327–39. http://dx.doi.org/10.5831/hmj.2007.29.3.327.

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20

Casali, Maria Rita, and Carlo Gagliardi. "Classifying PL $5$-manifolds up to regular genus seven." Proceedings of the American Mathematical Society 120, no. 1 (January 1, 1994): 275. http://dx.doi.org/10.1090/s0002-9939-1994-1205484-4.

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21

Rudyak, Yu B. "Realization of homology classes of PL-manifolds with singularities." Mathematical Notes of the Academy of Sciences of the USSR 41, no. 5 (May 1987): 417–22. http://dx.doi.org/10.1007/bf01159869.

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22

Jaco, William, and J. Hyam Rubinstein. "PL equivariant surgery and invariant decompositions of 3-manifolds." Advances in Mathematics 73, no. 2 (February 1989): 149–91. http://dx.doi.org/10.1016/0001-8708(89)90067-4.

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23

Chiavacci, Rossana, and Giuseppe Pareschi. "Some bounds for the regular genus of PL-manifolds." Discrete Mathematics 82, no. 2 (June 1990): 165–80. http://dx.doi.org/10.1016/0012-365x(90)90323-a.

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24

Daverman, Robert J. "Manifolds that induce approximate fibrations in the PL category." Topology and its Applications 66, no. 3 (October 1995): 267–97. http://dx.doi.org/10.1016/0166-8641(95)00051-h.

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25

Grunert, Romain, Wolfgang Kühnel, and Günter Rote. "PL Morse theory in low dimensions." Advances in Geometry 23, no. 1 (January 1, 2023): 135–50. http://dx.doi.org/10.1515/advgeom-2022-0027.

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Анотація:

Abstract We discuss a PL analog of Morse theory for PL manifolds. There are several notions of regular and critical points. A point is homologically regular if the homology does not change when passing through its level; it is strongly regular if the function can serve as one coordinate in a chart. Several criteria for strong regularity are presented. In particular, we show that in dimensions d ≤ 4 a homologically regular point on a PL d-manifold is always strongly regular. Examples show that this fails in higher dimensions d ≥ 5. One of our constructions involves an embedding of the dunce hat into 4-space and Mazur’s contractible 4-manifold. Finally, decidability questions in this context are discussed.

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26

Im, Young-Ho, and Yong-Kuk Kim. "PARTIALLY ASHPHERICAL MANIFOLDS WITH NONZERO EULER CHARACTERISTIC AS PL FIBRATORS." Journal of the Korean Mathematical Society 43, no. 1 (January 1, 2006): 99–109. http://dx.doi.org/10.4134/jkms.2006.43.1.099.

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27

Attene, Marco, Daniela Giorgi, Massimo Ferri, and Bianca Falcidieno. "On converting sets of tetrahedra to combinatorial and PL manifolds." Computer Aided Geometric Design 26, no. 8 (November 2009): 850–64. http://dx.doi.org/10.1016/j.cagd.2009.06.002.

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28

Casali, Maria Rita. "A note about bistellar operations on PL-manifolds with boundary." Geometriae Dedicata 56, no. 3 (July 1995): 257–62. http://dx.doi.org/10.1007/bf01263566.

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29

ASKITAS, N. "A NOTE ON THE #-UNKNOTTING OPERATION." Journal of Knot Theory and Its Ramifications 07, no. 06 (September 1998): 713–18. http://dx.doi.org/10.1142/s0218216598000371.

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Анотація:

We use a connection between local moves on knots and the singularity type of certain PL-spheres in 4-manifolds and use it to recover (stronger in principle versions of) known results as well as obtain new ones regarding certain #-unknotting numbers of knots.

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30

CASALI, MARIA RITA. "FROM FRAMED LINKS TO CRYSTALLIZATIONS OF BOUNDED 4-MANIFOLDS." Journal of Knot Theory and Its Ramifications 09, no. 04 (June 2000): 443–58. http://dx.doi.org/10.1142/s0218216500000220.

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Анотація:

It is well-known that every 3-manifold M3 may be represented by a framed link (L,c), which indicates the Dehn-surgery from [Formula: see text] to M3 = M3(L,c); moreover, M3 is the boundary of a PL 4-manifold M4 = M4(L, c), which is obtained from [Formula: see text] by adding 2-handles along the framed link (L, c). In this paper we study the relationships between the above representations and the representation theory of general PL-manifolds by edge-coloured graphs: in particular, we describe how to construct a 5-coloured graph representing M4=M4(L,c), directly from a planar diagram of (L,c). As a consequence, relations between the combinatorial properties of the link L and both the Heegaard genus of M3=M3(L,c) and the regular genus of M4=M4(L,c) are obtained.

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31

Korepanov, Igor G. "Invariants of PL Manifolds from Metrized Simplicial Complexes. Three-Dimensional Case." Journal of Nonlinear Mathematical Physics 8, no. 2 (January 2001): 196–210. http://dx.doi.org/10.2991/jnmp.2001.8.2.3.

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32

Cavicchioli, Alberto, and Friedrich Hegenbarth. "On the determination of PL-manifolds by handles of lower dimension." Topology and its Applications 53, no. 2 (November 1993): 111–18. http://dx.doi.org/10.1016/0166-8641(93)90131-v.

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33

Ferri, M., C. Gagliardi, and L. Grasselli. "A graph-theoretical representation of PL-manifolds — A survey on crystallizations." Aequationes Mathematicae 31, no. 1 (December 1986): 121–41. http://dx.doi.org/10.1007/bf02188181.

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34

Kato, Hisao. "Takens-type reconstruction theorems of one-sided dynamical systems." Nonlinearity 36, no. 3 (February 1, 2023): 1571–92. http://dx.doi.org/10.1088/1361-6544/acb396.

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Анотація:

Abstract The reconstruction theorem deals with dynamical systems that are given by a map T : X → X of a compact metric space X together with an observable f : X → R from X to the real line R . In 1981, by use of Whitney’s embedding theorem, Takens proved that if T : M → M is a (two-sided) diffeomorphism on a compact smooth manifold M with dim M = d , for generic (T, f) there is a bijection between elements x ∈ M and corresponding sequence ( f T j ( x ) ) j = 0 2 d , and moreover, in 2002 Takens proved a generalised version for endomorphisms. In natural sciences and physical engineering, there has been an increase in importance of fractal sets and more complicated spaces, and also in mathematics, many topological and dynamical properties and stochastic analysis of such spaces have been studied. In the present paper, by use of some topological methods we extend the Takens’ reconstruction theorems of compact smooth manifolds to reconstruction theorems of ‘non-invertible’ dynamical systems for a large class of compact metric spaces, which contains PL-manifolds, manifolds with branched structures and some fractal sets, e.g. Menger manifolds, Sierpiński carpet and Sierpiński gasket and dendrites, etc.

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35

McClure, J. E. "Erratum for the paper ‘On the chain-level intersection pairing for PL manifolds’." Geometry & Topology 13, no. 3 (March 12, 2009): 1775–77. http://dx.doi.org/10.2140/gt.2009.13.1775.

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36

Hillman, Jonathan A. "On 4-manifolds with universal covering space a compact geometric manifold." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 55, no. 2 (October 1993): 137–48. http://dx.doi.org/10.1017/s1446788700032006.

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Анотація:

AbstractThere are 11 closed 4-manifolds which admit geometries of compact type (S4, CP2 or S2 × S2) and two other closely related bundle spaces (S2 × S2 and the total space of the nontrivial RP2-bundle over S2). We show that the homotopy type of such a manifold is determined up to an ambiguity of order at most 4 by its quadratic 2-type, and this in turn is (in most cases) determined by the Euler characteristic, fundamental group and Stiefel-Whitney classes. In (at least) seven of the 13 cases, a PL 4-manifold with the same invariants as a geometric manifold or bundle space must be homeomorphic to it.

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37

Dimovski, D. "Canonical embeddings ofS1×Δn−1into orientable n -dimensional closed PL manifolds forn>4". Topology and its Applications 160, № 17 (листопад 2013): 2141–69. http://dx.doi.org/10.1016/j.topol.2013.08.015.

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38

Cao, Jianguo, and José F. Escobar. "A New 3-dimensional Curvature Integral Formula for PL-manifolds of Non-positive Curvature." Communications in Analysis and Geometry 11, no. 3 (2003): 489–551. http://dx.doi.org/10.4310/cag.2003.v11.n3.a4.

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39

Kamau-Devers, Gathoni, Gail Jardine, and David Yetter. "A general state-sum construction of 2-dimensional topological quantum field theories with defects." Journal of Knot Theory and Its Ramifications 26, no. 04 (April 2017): 1750014. http://dx.doi.org/10.1142/s0218216517500146.

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Анотація:

We derive a general state sum construction for 2D topological quantum field theories (TQFTs) with source defects on oriented curves, extending the state-sum construction from special symmetric Frobenius algebra for 2D TQFTs without defects (cf. Lauda and Pfeiffer [State-sum construction of two-dimensional open-closed topological quantum field theories, J. Knot Theory Ramifications 16 (2007) 1121–1163, doi: 10.1142/S0218216507005725]). From the extended Pachner moves (Crane and Yetter [Moves on filtered PL manifolds and stratified PL spaces, arXiv:1404.3142 ]), we derive equations that we subsequently translate into string diagrams so that we can easily observe their properties. As in Dougherty, Park and Yetter [On 2-dimensional Dijkgraaf–Witten theory with defects, to appear in J. Knots Theory Ramifications], we require that triangulations be flaglike, meaning that each simplex of the triangulation is either disjoint from the defect curve, or intersects it in a closed face, and that the extended Pachner moves preserve flaglikeness.

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40

Weiss, Michael. "Friedhelm Waldhausen, Bjørn Jahren, John Rognes: “Spaces of PL Manifolds and Categories of Simple Maps”." Jahresbericht der Deutschen Mathematiker-Vereinigung 115, no. 3-4 (December 3, 2013): 223–28. http://dx.doi.org/10.1365/s13291-013-0074-2.

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41

Alpern, S., and V. Prasad. "End Behaviour and Ergodicity for Homeomorphisms of Manifolds with Finitely Many Ends." Canadian Journal of Mathematics 39, no. 2 (April 1, 1987): 473–91. http://dx.doi.org/10.4153/cjm-1987-020-5.

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Анотація:

The recent paper of Berlanga and Epstein [5] demonstrated the significant role played by the “ends” of a noncompact manifold M in answering questions relating homeomorphisms of M to measures on M. In this paper we show that an analysis of the end behaviour of measure preserving homeomorphisms of a manifold also leads to an understanding of some of their ergodic properties, and allows results previously obtained for compact manifolds to be extended (with qualifications) to the noncompact case. We will show that ergodicity is typical (dense Gδ) with respect to various compact-open topology closed subsets of the space consisting of all homeomorphisms of a manifold M which preserve a measure μ. It may be interesting for topologists to note that we prove when M is a σ-compact connected n-manifold, n≧ 2, then M is the countable union of an increasing family of compact connected manifolds. If M is a PL or smooth manifold, this is well known and easy. If M is just, however, a topological n-manifold then we apply the recent results [9] and [12] to prove the result. The Borel measure μ, is taken to be nonatomic, locally finite, positive on open sets, and zero for the manifold boundary of M.

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42

Akita, Toshiyuki. "Euler Characteristics of Coxeter Groups, PL-Triangulations of Closed Manifolds, and Cohomology of Subgroups of Artin Groups." Journal of the London Mathematical Society 61, no. 3 (June 2000): 721–36. http://dx.doi.org/10.1112/s0024610700008693.

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43

KOBERDA, THOMAS, and YASH LODHA. "2-chains and square roots of Thompson’s group." Ergodic Theory and Dynamical Systems 40, no. 9 (March 25, 2019): 2515–32. http://dx.doi.org/10.1017/etds.2019.14.

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Анотація:

We study 2-generated subgroups $\langle f,g\rangle <\operatorname{Homeo}^{+}(I)$ such that $\langle f^{2},g^{2}\rangle$ is isomorphic to Thompson’s group $F$, and such that the supports of $f$ and $g$ form a chain of two intervals. We show that this class contains uncountably many isomorphism types. These include examples with non-abelian free subgroups, examples which do not admit faithful actions by $C^{2}$ diffeomorphisms on 1-manifolds, examples which do not admit faithful actions by $PL$ homeomorphisms on an interval, and examples which are not finitely presented. We thus answer questions due to Brin. We also show that many relatively uncomplicated groups of homeomorphisms can have very complicated square roots, thus establishing the behavior of square roots of $F$ as part of a general phenomenon among subgroups of $\operatorname{Homeo}^{+}(I)$.

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44

Pavešić, Petar. "Triangulations with few vertices of manifolds with non-free fundamental group." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149, no. 6 (January 15, 2019): 1453–63. http://dx.doi.org/10.1017/prm.2018.136.

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Анотація:

AbstractWe study lower bounds for the number of vertices in a PL-triangulation of a given manifold M. While most of the previous estimates are based on the dimension and the connectivity of M, we show that further information can be extracted by studying the structure of the fundamental group of M and applying techniques from the Lusternik-Schnirelmann category theory. In particular, we prove that every PL-triangulation of a d-dimensional manifold (d ⩾ 3) whose fundamental group is not free has at least 3d + 1 vertices. As a corollary, every d-dimensional homology sphere that admits a combinatorial triangulation with less than 3d vertices is PL-homeomorphic to Sd. Another important consequence is that every triangulation with small links of M is combinatorial.

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45

Ferri, Massimo. "Colour Switching and Homeomorphism of Manifolds." Canadian Journal of Mathematics 39, no. 1 (February 1, 1987): 8–32. http://dx.doi.org/10.4153/cjm-1987-002-5.

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Анотація:

Throughout this paper, we work in the PL and pseudosimplicial categories, for which we refer to [17] and [10] respectively. For the graph theory involved see [9].An h-coloured graph (Γ, γ) is a multigraph Γ = (V(Γ), E(Γ)) regular of degree h, endowed with an edge-coloration γ by h colours. If is the colour set, for each we setFor each set . For n ∊ Z, n ≧ 1, setΔn will be mostly used to denote the colour set for an (n + 1)-coloured graph.

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46

Sabourau, Stéphane. "Volume of minimal hypersurfaces in manifolds with nonnegative Ricci curvature." Journal für die reine und angewandte Mathematik (Crelles Journal) 2017, no. 731 (January 1, 2017): 1–19. http://dx.doi.org/10.1515/crelle-2014-0147.

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Анотація:

AbstractWe establish a min-max estimate on the volume width of a closed Riemannian manifold with nonnegative Ricci curvature. More precisely, we show that every closed Riemannian manifold with nonnegative Ricci curvature admits a PL Morse function whose level set volume is bounded in terms of the volume of the manifold. As a consequence of this sweep-out estimate, there exists an embedded, closed (possibly singular) minimal hypersurface whose volume is bounded in terms of the volume of the manifold.

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47

Casali, Maria Rita, and Paola Cristofori. "Cataloguing PL 4-Manifolds by Gem-Complexity." Electronic Journal of Combinatorics 22, no. 4 (November 13, 2015). http://dx.doi.org/10.37236/4749.

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Анотація:

We describe an algorithm to subdivide automatically a given set of PL $n$-manifolds (via coloured triangulations or, equivalently, via crystallizations) into classes whose elements are PL-homeomorphic. The algorithm, implemented in the case n=4, succeeds to solve completely the PL-homeomorphism problem among the catalogue of all closed connected PL 4-manifolds up to gem-complexity 8 (i.e., which admit a coloured triangulation with at most 18 4-simplices).Possible interactions with the (not completely known) relationship among different classification in TOP and DIFF=PL categories are also investigated. As a first consequence of the above PL classification, the non-existence of exotic PL 4-manifolds up to gem-complexity 8 is proved. Further applications of the tool are described, related to possible PL-recognition of different triangulations of the K3-surface.

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48

Basak, Biplab, and Jonathan Spreer. "Simple crystallizations of 4-manifolds." Advances in Geometry 16, no. 1 (January 1, 2016). http://dx.doi.org/10.1515/advgeom-2015-0043.

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AbstractMinimal crystallizations of simply connected PL 4-manifolds are very natural objects. Many of their topological features are reflected in their combinatorial structure which, in addition, is preserved under the connected sum operation. We present a minimal crystallization of the standard PL K3 surface. In combination with known results this yields minimal crystallizations of all simply connected PL 4-manifolds of “standard” type, that is, all connected sums of ℂℙ

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49

Cavicchioli, Alberto, and Fulvia Spaggiari. "On Graph-Theoretical Invariants of Combinatorial Manifolds." Electronic Journal of Combinatorics 26, no. 3 (July 5, 2019). http://dx.doi.org/10.37236/7493.

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The goal of this paper is to give some theorems which relate to the problem of classifying combinatorial (resp. smooth) closed manifolds up to piecewise-linear (PL) homeomorphism. For this, we use the combinatorial approach to the topology of PL manifolds by means of a special kind of edge-colored graphs, called crystallizations. Within this representation theory, Bracho and Montejano introduced in 1987 a nonnegative numerical invariant, called the reduced complexity, for any closed $n$-dimensional PL manifold. Here we consider this invariant, and extend in this context the concept of average order first introduced by Luo and Stong in 1993, and successively investigated by Tamura in 1996 and 1998. Then we obtain some classification results for closed connected smooth low-dimensional manifolds according to reduced complexity and average order. Finally, we answer to a question posed by Trout in 2013.

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50

Boissonnat, Jean-Daniel, and Mathijs Wintraecken. "The Topological Correctness of PL Approximations of Isomanifolds." Foundations of Computational Mathematics, July 13, 2021. http://dx.doi.org/10.1007/s10208-021-09520-0.

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AbstractIsomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. manifolds defined as the zero set of some multivariate multivalued smooth function $$f: {\mathbb {R}}^d\rightarrow {\mathbb {R}}^{d-n}$$ f : R d → R d - n . A natural (and efficient) way to approximate an isomanifold is to consider its piecewise-linear (PL) approximation based on a triangulation $$\mathcal {T}$$ T of the ambient space $${\mathbb {R}}^d$$ R d . In this paper, we give conditions under which the PL approximation of an isomanifold is topologically equivalent to the isomanifold. The conditions are easy to satisfy in the sense that they can always be met by taking a sufficiently fine and thick triangulation $$\mathcal {T}$$ T . This contrasts with previous results on the triangulation of manifolds where, in arbitrary dimensions, delicate perturbations are needed to guarantee topological correctness, which leads to strong limitations in practice. We further give a bound on the Fréchet distance between the original isomanifold and its PL approximation. Finally, we show analogous results for the PL approximation of an isomanifold with boundary.

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