Torus Actions and Their Applications in Topology and Combinatorics - Couverture souple

American Mathematical Society

Couverture souple

ISBN 10 : 0821831860 ISBN 13 : 9780821831861

Editeur : American Mathematical Society, 2002

Synopsis

This book presents the study of torus actions on topological spaces that 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.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2002
• Langue: anglais
• ISBN 10: 0821831860
• ISBN 13: 9780821831861
• Reliure: Poche
• Nombre de pages: 144
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible