Softcover ISBN:  9780821831861 
Product Code:  ULECT/24 
List Price:  $39.00 
MAA Member Price:  $35.10 
AMS Member Price:  $31.20 
Electronic ISBN:  9781470421717 
Product Code:  ULECT/24.E 
List Price:  $36.00 
MAA Member Price:  $32.40 
AMS Member Price:  $28.80 

Book DetailsUniversity Lecture SeriesVolume: 24; 2002; 144 ppMSC: Primary 52; 57; 14; 13;
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.ReadershipGraduate students and research mathematicians interested in topology or combinatorics; topologists interested in combinatorial applications and vice versa.

Table of Contents

Chapters

Introduction

Chapter 1. Polytopes

Chapter 2. Topology and combinatorics of simplicial complexes

Chapter 3. Commutative and homological algebra of simplicial complexes

Chapter 4. Cubical complexes

Chapter 5. Toric and quasitoric manifolds

Chapter 6. Momentangle complexes

Chapter 7. Cohomology of momentangle complexes and combinatorics of triangulated manifolds

Chapter 8. Cohomology rings of subspace arrangement complements


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


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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.
Graduate students and research mathematicians interested in topology or combinatorics; topologists interested in combinatorial applications and vice versa.

Chapters

Introduction

Chapter 1. Polytopes

Chapter 2. Topology and combinatorics of simplicial complexes

Chapter 3. Commutative and homological algebra of simplicial complexes

Chapter 4. Cubical complexes

Chapter 5. Toric and quasitoric manifolds

Chapter 6. Momentangle complexes

Chapter 7. Cohomology of momentangle complexes and combinatorics of triangulated manifolds

Chapter 8. Cohomology rings of subspace arrangement complements

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