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Product Code:  SURV/204 
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Hardcover ISBN:  9781470422141 
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Hardcover ISBN:  9781470422141 
Product Code:  SURV/204 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470424992 
Product Code:  SURV/204.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9781470422141 
eBook ISBN:  9781470424992 
Product Code:  SURV/204.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 204; 2015; 518 ppMSC: Primary 13; 14; 32; 52; 53; 55; 57
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 momentangle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of momentangle manifolds relates to combinatorial geometry and algebraic geometry of toric varieties via the notion of a quasitoric manifold. Discovery of remarkable geometric structures on momentangle manifolds led to important connections with classical and modern areas of symplectic, Lagrangian, and nonKaehler complex geometry. A related categorical construction of momentangle 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.
ReadershipGraduate students and research mathematicians interested in algebraic topology.

Table of Contents

Chapters

Chapter 1. Geometry and combinatorics of polytopes

Chapter 2. Combinatorial structures

Chapter 3. Combinatorial algebra of face rings

Chapter 4. Momentangle complexes

Chapter 5. Toric varieties and manifolds

Chapter 6. Geometric structures on momentangle manifolds

Chapter 7. Halfdimensional torus actions

Chapter 8. Homotopy theory of polyhedral products

Chapter 9. Torus actions and complex cobordism

Appendix A. Commutative and homological algebra

Appendix B. Algebraic topology

Appendix C. Categorical constructions

Appendix D. Bordism and cobordism

Appendix E. Formal group laws and Hirzebruch genera


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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 momentangle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of momentangle manifolds relates to combinatorial geometry and algebraic geometry of toric varieties via the notion of a quasitoric manifold. Discovery of remarkable geometric structures on momentangle manifolds led to important connections with classical and modern areas of symplectic, Lagrangian, and nonKaehler complex geometry. A related categorical construction of momentangle 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.
Graduate students and research mathematicians interested in algebraic topology.

Chapters

Chapter 1. Geometry and combinatorics of polytopes

Chapter 2. Combinatorial structures

Chapter 3. Combinatorial algebra of face rings

Chapter 4. Momentangle complexes

Chapter 5. Toric varieties and manifolds

Chapter 6. Geometric structures on momentangle manifolds

Chapter 7. Halfdimensional torus actions

Chapter 8. Homotopy theory of polyhedral products

Chapter 9. Torus actions and complex cobordism

Appendix A. Commutative and homological algebra

Appendix B. Algebraic topology

Appendix C. Categorical constructions

Appendix D. Bordism and cobordism

Appendix E. Formal group laws and Hirzebruch genera