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Mathematics
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Algebraic and Geometric Topology
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Algebraic and Geometric Topology

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (31 October 2015) | Viewed by 7637

Special Issue Editor

Prof. Dr. Yuli B. Rudyak

E-Mail Website
Guest Editor
Department of Mathematics, University of Florida, 358 Little Hall, P.O. Box 118105, Gainesville, FL 32611-8105, USA
Interests: algebraic topology; differential topology; symplectic topology

Special Issue Information

Daer Colleagues,

Algebraic Topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphic or homotopical equivalence. In greater detail, in considering a functor from topological spaces for certain algebraic objects (groups, rings, etc.), you know that the non-isomorphic groups come from non-homeomorphic spaces. Thus, given two topological spaces, you can try to find enough functors that can distinguish the spaces.

So, on one hand, algebraic topology studies algebraic invariants (functors) in and of themselves. Here, we concern ourselves with homotopical and homological groups, variety (co)bordism theories, K-theories, and other generalized (co)homology theories, etc., and the task is to evaluate/estimate the algebraic invariants of topological spaces, as well as the relations between these invariants. On the other hand, we observe applications of algebraic topology to several extremals problems (i.e., Morse theory, Lusterink--Schnirelmann theory, isoparametric problems, and systolic inequalities), dynamical systems and symplectic topology, variety aspects of fixed points theories, etc. Also, recently, we  have observed applications of algebraic topology to data analysis, robotics, brain research, biochemistry, etc.

Yuli Rudyak
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • category weight
  • cobordism
  • generalized cohomology theories
  • Lusternik--Schnirelmann category
  • Massey products
  • Svarc genus

Published Papers (2 papers)

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Research

556 KiB  
Article
Dynamics and the Cohomology of Measured Laminations
by Carlos Meniño Cotón
Mathematics 2016, 4(1), 18; https://doi.org/10.3390/math4010018 - 15 Mar 2016
Viewed by 3340
Abstract
In this paper, the interconnection between the cohomology of measured group actions and the cohomology of measured laminations is explored, the latter being a generalization of the former for the case of discrete group actions and cocycles evaluated on abelian groups. This relation [...] Read more.
In this paper, the interconnection between the cohomology of measured group actions and the cohomology of measured laminations is explored, the latter being a generalization of the former for the case of discrete group actions and cocycles evaluated on abelian groups. This relation gives a rich interplay between these concepts. Several results can be adapted to this setting—for instance, Zimmer’s reduction of the coefficient group of bounded cocycles or Fustenberg’s cohomological obstruction for extending the ergodicity \(\mathbb{Z}\)-action to a skew product relative to an \(S^{1}\) evaluated cocycle. Another way to think about foliated cocycles is also shown, and a particular application is the characterization of the existence of certain classes of invariant measures for smooth foliations in terms of the \(L^{\infty}\)-cohomology class of the infinitesimal holonomy. Full article
(This article belongs to the Special Issue Algebraic and Geometric Topology)
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271 KiB  
Article
Multiplicative Expression for the Coefficient in Fermionic 3–3 Relation
by Igor Korepanov
Mathematics 2016, 4(1), 3; https://doi.org/10.3390/math4010003 - 20 Jan 2016
Cited by 2 | Viewed by 3305
Abstract
Recently, a family of fermionic relations were discovered corresponding to Pachner move 3–3 and parameterized by complex-valued 2-cocycles, where the weight of a pentachoron (4-simplex) is a Grassmann–Gaussian exponent. Here, the proportionality coefficient between Berezin integrals in the l.h.s. and r.h.s. of such [...] Read more.
Recently, a family of fermionic relations were discovered corresponding to Pachner move 3–3 and parameterized by complex-valued 2-cocycles, where the weight of a pentachoron (4-simplex) is a Grassmann–Gaussian exponent. Here, the proportionality coefficient between Berezin integrals in the l.h.s. and r.h.s. of such relations is written in a form multiplicative over simplices. Full article
(This article belongs to the Special Issue Algebraic and Geometric Topology)
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