Journal articles: 'Algebraic; Topological'

1

Swamy, U. M., and R. Seshagiri Rao. "Algebraic Topological Closure Operators." Southeast Asian Bulletin of Mathematics 26, no. 4 (June 2003): 669–78. http://dx.doi.org/10.1007/s100120200071.

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2

Kuijpers, Bart, Jan Paredaens, and Jan Van den Bussche. "Topological elementary equivalence of closed semi-algebraic sets in the real plane." Journal of Symbolic Logic 65, no. 4 (December 2000): 1530–55. http://dx.doi.org/10.2307/2695063.

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AbstractWe investigate topological properties of subsets S of the real plane, expressed by first-order logic sentences in the language of the reals augmented with a binary relation symbol for S. Two sets are called topologically elementary equivalent if they have the same such first-order topological properties. The contribution of this paper is a natural and effective characterization of topological elementary equivalence of closed semi-algebraic sets.

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Kalai, Gil, Isabella Novik, Francisco Santos, and Volkmar Welker. "Geometric, Algebraic, and Topological Combinatorics." Oberwolfach Reports 16, no. 3 (September 9, 2020): 2395–472. http://dx.doi.org/10.4171/owr/2019/39.

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Hernández-Arzusa, Julio, and Salvador Hernández. "Reflections in topological algebraic structures." Topology and its Applications 281 (August 2020): 107204. http://dx.doi.org/10.1016/j.topol.2020.107204.

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5

Chan, Onn, Ivan Gutman, Tao-Kai Lam, and Russell Merris. "Algebraic Connections between Topological Indices." Journal of Chemical Information and Computer Sciences 38, no. 1 (January 19, 1998): 62–65. http://dx.doi.org/10.1021/ci970059y.

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6

Meinke, Karl. "Topological methods for algebraic specification." Theoretical Computer Science 166, no. 1-2 (October 1996): 263–90. http://dx.doi.org/10.1016/0304-3975(95)00261-8.

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HINDMAN, NEIL. "The Topological-Algebraic System(?N, +, ?)." Annals of the New York Academy of Sciences 704, no. 1 Papers on Gen (December 1993): 155–63. http://dx.doi.org/10.1111/j.1749-6632.1993.tb52519.x.

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BẮnicẮ, Constantin, and Mihai Putinar. "On complex vector bundles on rational threefolds." Mathematical Proceedings of the Cambridge Philosophical Society 97, no. 2 (March 1985): 279–88. http://dx.doi.org/10.1017/s0305004100062824.

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It is known [14] that every topological complex vector bundle on a smooth rational surface admits an algebraic structure. In [10] one constructs algebraic vector bundles of rank 2 on with arbitrary Chern classes c1, c2 subject to the necessary topological condition c1 c2 = 0 (mod 2). However, in dimensions greater than 2 the Chern classes don't determine the topological type of a vector bundle. In [2] one classifies the topological complex vector bundles of rank 2 on and one proves that any such bundle admits an algebraic structure.

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Kucharz, Wojciech, and Krzysztof Kurdyka. "Stratified-algebraic vector bundles." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 745 (December 1, 2018): 105–54. http://dx.doi.org/10.1515/crelle-2015-0105.

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Abstract We investigate stratified-algebraic vector bundles on a real algebraic variety X. A stratification of X is a finite collection of pairwise disjoint, Zariski locally closed subvarieties whose union is X. A topological vector bundle ξ on X is called a stratified-algebraic vector bundle if, roughly speaking, there exists a stratification {\mathcal{S}} of X such that the restriction of ξ to each stratum S in {\mathcal{S}} is an algebraic vector bundle on S. In particular, every algebraic vector bundle on X is stratified-algebraic. It turns out that stratified-algebraic vector bundles have many surprising properties, which distinguish them from algebraic and topological vector bundles.

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10

HOSONO, SHINOBU. "ALGEBRAIC DEFINITION OF TOPOLOGICAL W GRAVITY." International Journal of Modern Physics A 07, no. 21 (August 20, 1992): 5193–211. http://dx.doi.org/10.1142/s0217751x92002374.

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We propose a definition of the topological W gravity using some properties of the principal three-dimensional subalgebra of a simple Lie algebra due to Kostant. In our definition, structures of the two-dimensional topological gravity are naturally embedded in the extended theories. In accordance with the definition, we will present some explicit calculations for the W3 gravity.

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11

Ballico, E. "On vector bundles on algebraic surfaces and 0-cycles." Nagoya Mathematical Journal 130 (June 1993): 19–23. http://dx.doi.org/10.1017/s0027763000004402.

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Let X be an algebraic complex projective surface equipped with the euclidean topology and E a rank 2 topological vector bundle on X. It is a classical theorem of Wu ([Wu]) that E is uniquely determined by its topological Chern classes . Viceversa, again a classical theorem of Wu ([Wu]) states that every pair (a, b) ∈ (H (X, Z), Z) arises as topological Chern classes of a rank 2 topological vector bundle. For these results the existence of an algebraic structure on X was not important; for instance it would have been sufficient to have on X a holomorphic structure. In [Sch] it was proved that for algebraic X any such topological vector bundle on X has a holomorphic structure (or, equivalently by GAGA an algebraic structure) if its determinant line bundle has a holomorphic structure. It came as a surprise when Elencwajg and Forster ([EF]) showed that sometimes this was not true if we do not assume that X has an algebraic structure but only a holomorphic one (even for some two dimensional tori (see also [BL], [BF], or [T])).

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12

Insall, Matt. "Hyperalgebraic primitive elements for relational algebraic and topological algebraic models." Studia Logica 57, no. 2-3 (October 1996): 409–18. http://dx.doi.org/10.1007/bf00370842.

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13

Arkhangel'skii, A. V. "Algebraic objects generated by topological structure." Journal of Soviet Mathematics 45, no. 1 (April 1989): 956–90. http://dx.doi.org/10.1007/bf01094867.

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14

Cuartero, Bienvenido, and José E. Galé. "Bounded degree of algebraic topological algebras." Communications in Algebra 22, no. 1 (January 1994): 329–37. http://dx.doi.org/10.1080/00927879408824848.

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15

Rhodes, J., and P. Weil. "Algebraic and topological theory of languages." RAIRO - Theoretical Informatics and Applications 29, no. 1 (1995): 1–44. http://dx.doi.org/10.1051/ita/1995290100011.

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16

Scheiderer, Claus. "Algebraic subgroup lattices of topological groups." Algebra Universalis 22, no. 2-3 (June 1986): 235–43. http://dx.doi.org/10.1007/bf01224029.

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17

Burness, Timothy C., Spencer Gerhardt, and Robert M. Guralnick. "Topological generation of exceptional algebraic groups." Advances in Mathematics 369 (August 2020): 107177. http://dx.doi.org/10.1016/j.aim.2020.107177.

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18

DiCarlo, Antonio, Alberto Paoluzzi, and Vadim Shapiro. "Linear algebraic representation for topological structures." Computer-Aided Design 46 (January 2014): 269–74. http://dx.doi.org/10.1016/j.cad.2013.08.044.

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19

Dovermann, Karl Heinz, Friedrich Knop, and Dong Youp Suh. "Topological invariants of real algebraic actions." Topology and its Applications 40, no. 2 (July 1991): 171–88. http://dx.doi.org/10.1016/0166-8641(91)90049-r.

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20

Cortiñas, Guillermo, and Andreas Thom. "Algebraic geometry of topological spaces I." Acta Mathematica 209, no. 1 (2012): 83–131. http://dx.doi.org/10.1007/s11511-012-0082-6.

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21

Toyota, N. "On algebraic structures of topological gravity." Physics Letters B 282, no. 3-4 (May 1992): 314–20. http://dx.doi.org/10.1016/0370-2693(92)90645-k.

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22

MOSTAFAZADEH, A., and K. AGHABABAEI SAMANI. "TOPOLOGICAL SYMMETRIES." Modern Physics Letters A 15, no. 03 (January 30, 2000): 175–84. http://dx.doi.org/10.1142/s0217732300000177.

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We introduce the notion of a topological symmetry as a quantum mechanical symmetry involving a certain topological invariant. We obtain the underlying algebraic structure of the ℤ2-graded uniform topological symmetries of types (1, 1) and (2, 1). This leads to a novel derivation of the algebras of supersymmetry and p = 2 parasupersymmetry.

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23

Rodabaugh, S. E. "Relationship of Algebraic Theories to Powerset Theories and Fuzzy Topological Theories for Lattice-Valued Mathematics." International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–71. http://dx.doi.org/10.1155/2007/43645.

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This paper deals with a broad question—to what extent is topology algebraic—using two specific questions: (1) what are the algebraic conditions on the underlying membership lattices which insure that categories for topology and fuzzy topology are indeed topological categories; and (2) what are the algebraic conditions which insure that algebraic theories in the sense of Manes are a foundation for the powerset theories generating topological categories for topology and fuzzy topology? This paper answers the first question by generalizing the Höhle-Šostak foundations for fixed-basis lattice-valued topology and the Rodabaugh foundations for variable-basis lattice-valued topology using semi-quantales; and it answers the second question by giving necessary and sufficient conditions under which certain theories—the very ones generating powerset theories generating (fuzzy) topological theories in the sense of this paper—are algebraic theories, and these conditions use unital quantales. The algebraic conditions answering the second question are much stronger than those answering the first question. The syntactic benefits of having an algebraic theory as a foundation for the powerset theory underlying a (fuzzy) topological theory are explored; the relationship between these two specific questions is discussed; the role of pseudo-adjoints is identified in variable-basis powerset theories which are algebraically generated; the relationships between topological theories in the sense of Adámek-Herrlich-Strecker and topological theories in the sense of this paper are fully resolved; lower-image operators introduced for fixed-basis mathematics are completely described in terms of standard image operators; certain algebraic theories are given which determine powerset theories determining a new class of variable-basis categories for topology and fuzzy topology using new preimage operators; and the theories of this paper are undergirded throughout by several extensive inventories of examples.

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24

Krishna, Amalendu, and Jinhyun Park. "Algebraic cobordism theory attached to algebraic equivalence." Journal of K-Theory 11, no. 1 (February 2013): 73–112. http://dx.doi.org/10.1017/is013001028jkt210.

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AbstractBased on the algebraic cobordism theory of Levine and Morel, we develop a theory of algebraic cobordism modulo algebraic equivalence.We prove that this theory can reproduce Chow groups modulo algebraic equivalence and the semi-topological K0-groups. We also show that with finite coefficients, this theory agrees with the algebraic cobordism theory.We compute our cobordism theory for some low dimensional varieties. The results on infinite generation of some Griffiths groups by Clemens and on smash-nilpotence by Voevodsky and Voisin are also lifted and reinterpreted in terms of this cobordism theory.

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25

Fagnani, Fabio. "Some results on the classification of expansive automorphisms of compact abelian groups." Ergodic Theory and Dynamical Systems 16, no. 1 (February 1996): 45–50. http://dx.doi.org/10.1017/s0143385700008701.

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AbstractIn this paper we study expansive automorphisms of compact 0-dimensional abelian groups. Our main result is the complete algebraic and topological classification of the transitive expansive automorpisms for which the maximal order of the elements isp2for a primep. This yields a classification of the transitive expansive automorphisms with topological entropy logp2. Finally, we prove a necessary and sufficient condition for an expansive automorphism to be conjugated, topologically and algebraically, to a shift over a finite group.

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26

Besana, Alberto, and Cristina Martínez. "A Topological View of Reed–Solomon Codes." Mathematics 9, no. 5 (March 9, 2021): 578. http://dx.doi.org/10.3390/math9050578.

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We studied a particular class of well known error-correcting codes known as Reed–Solomon codes. We constructed RS codes as algebraic-geometric codes from the normal rational curve. This approach allowed us to study some algebraic representations of RS codes through the study of the general linear group GL(n,q). We characterized the coefficients that appear in the decompostion of an irreducible representation of the special linear group in terms of Gromov–Witten invariants of the Hilbert scheme of points in the plane. In addition, we classified all the algebraic codes defined over the normal rational curve, thereby providing an algorithm to compute a set of generators of the ideal associated with any algebraic code constructed on the rational normal curve (NRC) over an extension Fqn of Fq.

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27

Bagchi, Susmit. "Analysis of Topological Endomorphism of Fuzzy Measure in Hausdorff Distributed Monoid Spaces." Symmetry 11, no. 5 (May 15, 2019): 671. http://dx.doi.org/10.3390/sym11050671.

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The concepts of fuzzy sets and topology are widely applied to model various algebraic structures and computations. The dynamics of fuzzy measures in topological spaces having distributed monoid embeddings is an interesting topic in the presence of topological endomorphism. This paper presents the analysis of topological endomorphism and the properties of topological fuzzy measures in distributed monoid spaces. The topological space is considered to be Hausdorff and second countable in nature. The analysis of consistency of fuzzy measure in endomorphic topological spaces is formulated. The algebraic structures of endomorphic topological spaces having distributed cyclic monoids are constructed. The cyclic monoids contain specific generators, and a related cyclic topological endomorphism within the subspace is formulated. The analytical properties of fuzzy topological measures in the presence of cyclic topological endomorphism are presented. A comparative analysis of this proposed work with other related work in the domain is included.

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28

Marín, David, Jean-François Mattei, and Éliane Salem. "Topological Moduli Space for Germs of Holomorphic Foliations." International Mathematics Research Notices 2020, no. 23 (October 31, 2018): 9228–92. http://dx.doi.org/10.1093/imrn/rny244.

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Abstract This work deals with the topological classification of germs of singular foliations on $(\mathbb{C}^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho–Sad indices, and the projective holonomy representations and we compute the moduli space of topological classes in terms of the cohomology of a new algebraic object that we call group-graph. This moduli space may be an infinite-dimensional functional space but under generic conditions we prove that it has finite dimension and we describe its algebraic and topological structure.

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29

Milani, Vida, Seyed M. H. Mansourbeigi, and Hossein Finizadeh. "Algebraic and topological structures on rational tangles." Applied General Topology 18, no. 1 (April 3, 2017): 1. http://dx.doi.org/10.4995/agt.2017.2250.

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<p>In this paper we present the construction of a group Hopf algebra on the class of rational tangles. A locally finite partial order on this class is introduced and a topology is generated. An interval coalgebra structure associated with the locally finite partial order is specified. Irrational and real tangles are introduced and their relation with rational tangles are studied. The existence of the maximal real tangle is described in detail.</p>

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30

Hadzihasanovic, Amar. "A Topological Perspective on Interacting Algebraic Theories." Electronic Proceedings in Theoretical Computer Science 236 (January 1, 2017): 70–86. http://dx.doi.org/10.4204/eptcs.236.5.

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31

Peng, Chuang. "Algebraic and topological entropy on lie groups." Mathematical and Computer Modelling 39, no. 1 (January 2004): 13–19. http://dx.doi.org/10.1016/s0895-7177(04)90502-x.

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32

Malykhin, V. I. "An algebraic isomorphism that is not topological." Russian Mathematical Surveys 40, no. 6 (December 31, 1985): 135–36. http://dx.doi.org/10.1070/rm1985v040n06abeh003715.

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33

Lima-Filho, Paulo. "The topological group structure of algebraic cycles." Duke Mathematical Journal 75, no. 2 (August 1994): 467–91. http://dx.doi.org/10.1215/s0012-7094-94-07513-3.

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34

Dikranjan, Dikran, and Anna Giordano Bruno. "The connection between topological and algebraic entropy." Topology and its Applications 159, no. 13 (August 2012): 2980–89. http://dx.doi.org/10.1016/j.topol.2012.05.009.

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35

Eynard, B., and N. Orantin. "Invariants of algebraic curves and topological expansion." Communications in Number Theory and Physics 1, no. 2 (2007): 347–452. http://dx.doi.org/10.4310/cntp.2007.v1.n2.a4.

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36

De Loera, Jesús A. "Algebraic, Geometric, and Topological Methods in Optimization." Notices of the American Mathematical Society 66, no. 01 (January 1, 2019): 1. http://dx.doi.org/10.1090/noti1776.

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37

De Loera, Jesús A. "Algebraic and Topological Tools in Linear Optimization." Notices of the American Mathematical Society 66, no. 07 (August 1, 2019): 1. http://dx.doi.org/10.1090/noti1907.

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38

May, J. P. "Stable Algebraic Topology and Stable Topological Algebra." Bulletin of the London Mathematical Society 30, no. 3 (May 1998): 225–34. http://dx.doi.org/10.1112/s002460939700427x.

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39

Grigorchuk, R. I., and K. S. Medynets. "On algebraic properties of topological full groups." Sbornik: Mathematics 205, no. 6 (June 2014): 843–61. http://dx.doi.org/10.1070/sm2014v205n06abeh004400.

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40

Cheng, Jin-San, Xiao-Shan Gao, and Ming Li. "Intrinsic topological representation of real algebraic surfaces." ACM SIGSAM Bulletin 39, no. 3 (September 2005): 80–81. http://dx.doi.org/10.1145/1113439.1113444.

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41

Glebsky, L. Yu, E. I. Gordon, and C. Ward Henson. "On finite approximations of topological algebraic systems." Journal of Symbolic Logic 72, no. 1 (March 2007): 1–25. http://dx.doi.org/10.2178/jsl/1174668381.

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AbstractWe introduce and discuss a concept of approximation of a topological algebraic system A by finite algebraic systems from a given class . If A is discrete, this concept agrees with the familiar notion of a local embedding of A in a class of algebraic systems. One characterization of this concept states that A is locally embedded in iff it is a subsystem of an ultraproduct of systems from . In this paper we obtain a similar characterization of approximability of a locally compact system A by systems from using the language of nonstandard analysis.In the signature of A we introduce positive bounded formulas and their approximations; these are similar to those introduced by Henson [14] for Banach space structures (see also [15, 16]). We prove that a positive bounded formula φ holds in A if and only if all precise enough approximations of φ hold in all precise enough approximations of A.We also prove that a locally compact field cannot be approximated arbitrarily closely by finite (associative) rings (even if the rings are allowed to be non-commutative). Finite approximations of the field ℝ can be considered as possible computer systems for real arithmetic. Thus, our results show that there do not exist arbitrarily accurate computer arithmetics for the reals that are associative rings.

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42

Ustinov, Yu I. "Algebraic invariants of topological conjugacy of solenoids." Mathematical Notes of the Academy of Sciences of the USSR 42, no. 1 (July 1987): 583–90. http://dx.doi.org/10.1007/bf01138732.

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43

Vassiliev, V. A. "On topological invariants of real algebraic functions." Functional Analysis and Its Applications 45, no. 3 (September 2011): 163–72. http://dx.doi.org/10.1007/s10688-011-0020-y.

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44

Neumann, Eike, and Arno Pauly. "A topological view on algebraic computation models." Journal of Complexity 44 (February 2018): 1–22. http://dx.doi.org/10.1016/j.jco.2017.08.003.

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45

Sorella, S. P. "Algebraic characterization of the topological σ-model." Physics Letters B 228, no. 1 (September 1989): 69–74. http://dx.doi.org/10.1016/0370-2693(89)90527-3.

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46

Ausoni, Christian, and John Rognes. "Algebraic K-theory of topological K-theory." Acta Mathematica 188, no. 1 (2002): 1–39. http://dx.doi.org/10.1007/bf02392794.

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47

Sait Eroǧlu, Mehmet. "Algebraic characterization of some fuzzy topological spaces." Fuzzy Sets and Systems 47, no. 3 (May 1992): 377–80. http://dx.doi.org/10.1016/0165-0114(92)90302-k.

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48

Bujalance, E., J. J. Etayo, and J. M. Gamboa. "Topological types ofp-hyperelliptic real algebraic curves." Mathematische Zeitschrift 194, no. 2 (June 1987): 275–83. http://dx.doi.org/10.1007/bf01161975.

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49

CARLSSON, ERIK, GUNNAR CARLSSON, and VIN DE SILVA. "AN ALGEBRAIC TOPOLOGICAL METHOD FOR FEATURE IDENTIFICATION." International Journal of Computational Geometry & Applications 16, no. 04 (August 2006): 291–314. http://dx.doi.org/10.1142/s021819590600204x.

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We develop a mathematical framework for describing local features of a geometric object—such as the edges of a square or the apex of a cone—in terms of algebraic topological invariants. The main tool is the construction of a "tangent complex" for an arbitrary geometrical object, generalising the usual tangent bundle of a manifold. This framework can be used to develop algorithms for automatic feature location. We give several examples of applying such algorithms to geometric objects represented by point-cloud data sets.

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50

Lv, Quanjin, Xinghao Peng, Yuqing Wu, and Jiaying Zhang. "Algebraic and Topological Structures of Complex Numbers." Journal of Physics: Conference Series 2012, no. 1 (September 1, 2021): 012071. http://dx.doi.org/10.1088/1742-6596/2012/1/012071.

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Journal articles on the topic 'Algebraic; Topological'

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