Torus Actions and Their Applications in Topology and Combinatorics is popular PDF and ePub book, written by V. M. Buchstaber in 2002, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Torus Actions and Their Applications in Topology and Combinatorics can be Read Online from any device for your convenience.
Torus Actions and Their Applications in Topology and Combinatorics Book PDF Summary
Here, the study of torus actions on topological spaces is presented as a bridge connecting combinatorial and convex geometry with commutative and homological algebra, algebraic geometry, and topology. This established link helps in understanding the geometry and topology of a space with torus action by studying the combinatorics of the space of orbits. Conversely, subtle properties of a combinatorial object can be realized by interpreting it as the orbit structure for a propermanifold or as a complex acted on by a torus. The latter can be a symplectic manifold with Hamiltonian torus action, a toric variety or manifold, a subspace arrangement complement, etc., while the combinatorial objects include simplicial and cubical complexes, polytopes, and arrangements. This approachalso provides a natural topological interpretation in terms of torus actions of many constructions from commutative and homological algebra used in combinatorics. The exposition centers around the theory of moment-angle complexes, providing an effective way to study invariants of triangulations by methods of equivariant topology. The book includes many new and well-known open problems and would be suitable as a textbook. It will be useful for specialists both in topology and in combinatoricsand will help to establish even tighter connections between the subjects involved.
Detail Book of Torus Actions and Their Applications in Topology and Combinatorics PDF
- Author : V. M. Buchstaber
- Release : 01 October 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821831861
- Genre : Mathematics
- Total Page : 154 pages
- Language : English
- PDF File Size : 13,7 Mb
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