Special Issue "Algebraic and Geometric Topology"
A special issue of Mathematics (ISSN 2227-7390).
Deadline for manuscript submissions: closed (31 October 2015).
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.
Manuscript Submission Information
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- category weight
- generalized cohomology theories
- Lusternik--Schnirelmann category
- Massey products
- Svarc genus