University Lecture Series 2002; 144 pp; softcover Volume: 24 ISBN10: 0821831860 ISBN13: 9780821831861 List Price: US$36 Member Price: US$28.80 Order Code: ULECT/24
 The book presents 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 momentangle complexes, providing an effective way to study invariants of triangulations by methods of equivariant topology. The book includes many new and wellknown 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. Readership Graduate students and research mathematicians interested in topology or combinatorics; topologists interested in combinatorial applications and vice versa. Reviews "The book is quite wellwritten and includes many new and wellknown open problems"  Mathematical Reviews "The text contains a wealth of material and ... the book may be a welcome collection for researchers in the field and a useful overview of the literature for novices."  Zentralblatt MATH Table of Contents  Introduction
 Polytopes
 Topology and combinatorics of simplicial complexes
 Commutative and homological algebra of simplicial complexes
 Cubical complexes
 Toric and quasitoric manifolds
 Momentangle complexes
 Cohomology of momentangle complexes and combinatorics of triangulated manifolds
 Cohomology rings of subspace arrangement complements
 Bibliography
 Index
