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Relevant bibliographies by topics / PL-manifolds

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Academic literature on the topic 'PL-manifolds'

Author: Grafiati

Published: 14 March 2023

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Journal articles on the topic "PL-manifolds"

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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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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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "PL-manifolds"

1

Carbone, Gaspare. "Invariants of N-Dimensional PL-Manifolds from the (Re)Coupling of Angular Momenta." Doctoral thesis, SISSA, 2000. http://hdl.handle.net/20.500.11767/4229.

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Vasilevska, Violeta. "Fibrator properties of PL manifolds." 2004. http://etd.utk.edu/2004/VasilevskaVioleta.pdf.

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Thesis (Ph. D.)--University of Tennessee, Knoxville, 2004.
Title from title page screen (viewed Sept. 23, 2004). Thesis advisor: Robert J. Daverman. Document formatted into pages (ix, 71 p.). Vita. Includes bibliographical references (p. 64-67).

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Books on the topic "PL-manifolds"

1

Jaco, William H., Hyam Rubinstein, Craig David Hodgson, Martin Scharlemann, and Stephan Tillmann. Geometry and topology down under: A conference in honour of Hyam Rubinstein, July 11-22, 2011, The University of Melbourne, Parkville, Australia. Providence, Rhode Island: American Mathematical Society, 2013.

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1968-, Goryunov Victor, Houston Kevin 1968-, and Wik-Atique Roberta 1964-, eds. Real and complex singularities: XI International Workshop on Real and Complex Singularities, July 27-August 1, 2010, Universidade de São Paulo, São Carlos, SP Brazil. Providence, R.I: American Mathematical Society, 2012.

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3

1974-, Nelson Sam, ed. Quandles: An introduction to the algebra of knots. Providence, Rhode Island: American Mathematical Society, 2015.

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4

Spaces of PL Manifolds and Categories of Simple Maps. Princeton University Press, 2013.

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5

Rognes, John, Friedhelm Waldhausen, and Bjö Jahren. Spaces of PL Manifolds and Categories of Simple Maps (Am-186). Princeton University Press, 2013.

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Rognes, John, Friedhelm Waldhausen, and Bjø Jahren. Spaces of PL Manifolds and Categories of Simple Maps (AM-186). Princeton University Press, 2013.

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Rognes, John, Friedhelm Waldhausen, and Bjø Jahren. Spaces of PL Manifolds and Categories of Simple Maps (AM-186). Princeton University Press, 2013.

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8

Introduction to 3-maniflods. AMS, 2014.

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9

Hyperbolic Knot Theory. American Mathematical Society, 2020.

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10

On Groups of PL-Homeomorphisms of the Real Line. American Mathematical Society, 2016.

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Book chapters on the topic "PL-manifolds"

1

Allgower, Eugene L., and Kurt Georg. "General PL Algorithms on PL Manifolds." In Numerical Continuation Methods, 203–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-61257-2_14.

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2

Davis, Michael W., and Jean-Claude Hausmann. "Aspherical manifolds without smooth or PL structure." In Lecture Notes in Mathematics, 135–42. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0085224.

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3

Waldhausen, Friedhelm, Bjørn Jahren, and John Rognes. "The stable parametrized h-cobordism theorem." In Spaces of PL Manifolds and Categories of Simple Maps (AM-186). Princeton University Press, 2013. http://dx.doi.org/10.23943/princeton/9780691157757.003.0002.

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This chapter deals with the stable parametrized h-cobordism theorem. It begins with a discussion of the manifold part; here DIFF is written for the category of Csuperscript infinity smooth manifolds, PL for the category of piecewise-linear manifolds, and TOP for the category of topological manifolds. CAT is generically written for any one of these geometric categories. Relevant terms such as stabilization map, simple map, pullback map, PL Serre fibrations, weak homotopy equivalence, PL Whitehead space, and cofibration are also defined. The chapter proceeds by describing the non-manifold part, the algebraic K-theory of spaces, and the relevance of simple maps to the study of PL homeomorphisms of manifolds.

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"14. General PL Algorithms on PL Manifolds." In Introduction to Numerical Continuation Methods, 203–32. Society for Industrial and Applied Mathematics, 2003. http://dx.doi.org/10.1137/1.9780898719154.ch14.

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Waldhausen, Friedhelm, Bjørn Jahren, and John Rognes. "The manifold part." In Spaces of PL Manifolds and Categories of Simple Maps (AM-186). Princeton University Press, 2013. http://dx.doi.org/10.23943/princeton/9780691157757.003.0005.

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This chapter reduces the proof of the manifold part of the stable parametrized h-cobordism theorem to a result about spaces of stably framed manifolds. Here Δ‎superscript q denotes the standard affine q-simplex. All polyhedra will be compact, and all manifolds considered will be compact PL manifolds. The chapter begins with a discussion of spaces of PL manifolds. It defines a space of manifolds as a simplicial set, with families of manifolds parametrized by Δ‎superscript q as the q-simplices. Relevant terms such as tangent microbundle, fiberwise tangent microbundle, stably framed family of manifolds, and space of stably framed n-manifolds are taken into account. The chapter also describes the spaces of thickenings and how to straighten the thickenings.

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Waldhausen, Friedhelm, Bjørn Jahren, and John Rognes. "Introduction." In Spaces of PL Manifolds and Categories of Simple Maps (AM-186). Princeton University Press, 2013. http://dx.doi.org/10.23943/princeton/9780691157757.003.0001.

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This book presents a proof of the stable parametrized h-cobordism theorem, which deals with the existence of a natural homotopy equivalence for each compact CAT manifold. In this theorem, a stable CAT h-cobordism space is defined in terms of manifolds, whereas a CAT Whitehead space is defined in terms of algebraic K-theory. This is a stable range extension to parametrized families of the classical hand s-cobordism theorems first stated by A. E. Hatcher, but his proofs were incomplete. This book provides a full proof of this key result, which provides the link between the geometric topology of high-dimensional manifolds and their automorphisms, as well as the algebraic K-theory of spaces and structured ring spectra.

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"Introduction." In Spaces of PL Manifolds and Categories of Simple Maps (AM-186), 1–6. Princeton University Press, 2013. http://dx.doi.org/10.1515/9781400846528-001.

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"1. The stable parametrized h-cobordism theorem." In Spaces of PL Manifolds and Categories of Simple Maps (AM-186), 7–28. Princeton University Press, 2013. http://dx.doi.org/10.1515/9781400846528-002.

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"2. On simple maps." In Spaces of PL Manifolds and Categories of Simple Maps (AM-186), 29–98. Princeton University Press, 2013. http://dx.doi.org/10.1515/9781400846528-003.

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10

"3. The non-manifold part." In Spaces of PL Manifolds and Categories of Simple Maps (AM-186), 99–138. Princeton University Press, 2013. http://dx.doi.org/10.1515/9781400846528-004.

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