**Mathematical Surveys and Monographs**

Volume: 204;
2015;
518 pp;
Hardcover

MSC: Primary 13; 14; 32; 52; 53; 55; 57;

Print ISBN: 978-1-4704-2214-1

Product Code: SURV/204

List Price: $110.00

Individual Member Price: $88.00

**Electronic ISBN: 978-1-4704-2499-2
Product Code: SURV/204.E**

List Price: $110.00

Individual Member Price: $88.00

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#### Supplemental Materials

# Toric Topology

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*Victor M. Buchstaber; Taras E. Panov*

This book is about toric topology, a new area
of mathematics that emerged at the end of the 1990s on the border of
equivariant topology, algebraic and symplectic geometry,
combinatorics, and commutative algebra. It has quickly grown into a
very active area with many links to other areas of mathematics, and
continues to attract experts from different fields.

The key players in toric topology are moment-angle manifolds, a
class of manifolds with torus actions defined in combinatorial
terms. Construction of moment-angle manifolds relates to combinatorial
geometry and algebraic geometry of toric varieties via the notion of a
quasitoric manifold. Discovery of remarkable geometric structures on
moment-angle manifolds led to important connections with classical and
modern areas of symplectic, Lagrangian, and non-Kaehler complex
geometry. A related categorical construction of moment-angle
complexes and polyhedral products provides for a universal framework
for many fundamental constructions of homotopical topology. The study
of polyhedral products is now evolving into a separate subject of
homotopy theory. A new perspective on torus actions has also
contributed to the development of classical areas of algebraic
topology, such as complex cobordism.

This book includes many open problems and is addressed to experts
interested in new ideas linking all the subjects involved, as well as
to graduate students and young researchers ready to enter this
beautiful new area.

#### Table of Contents

# Table of Contents

## Toric Topology

- Cover Cover11
- Title page iii4
- Contents v6
- Introduction ix10
- Chapter 1. Geometry and combinatorics of polytopes 116
- Chapter 2. Combinatorial structures 5570
- Chapter 3. Combinatorial algebra of face rings 91106
- Chapter 4. Moment-angle complexes 129144
- Chapter 5. Toric varieties and manifolds 179194
- Chapter 6. Geometric structures on moment-angle manifolds 201216
- Chapter 7. Half-dimensional torus actions 239254
- Chapter 8. Homotopy theory of polyhedral products 313328
- Chapter 9. Torus actions and complex cobordism 347362
- Appendix A. Commutative and homological algebra 395410
- Appendix B. Algebraic topology 413428
- Appendix C. Categorical constructions 439454
- Appendix D. Bordism and cobordism 453468
- Appendix E. Formal group laws and Hirzebruch genera 473488
- Bibliography 495510
- Index 511526
- Back Cover Back Cover1534

#### Readership

Graduate students and research mathematicians interested in algebraic topology.