Torus Actions and their Applications in Topology and Combinatorics

Buchstaber, Victor and Panov, Taras (2002) Torus Actions and their Applications in Topology and Combinatorics. University Lecture Series number 24; OUP . American Mathematical Society. ISBN 10: 0-8218-3186-0

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Abstract

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 proper manifold 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 approach also 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 combinatorics and will help to establish even tighter connections between the subjects involved.

Item Type:	Book
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 55 Algebraic topology
Depositing User:	Ms Lucy van Russelt
Date Deposited:	23 Mar 2007
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/724

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