Toric topology / Victor M. Buchstaber, Taras E. Panov.

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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 mathemat...

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Bibliographic Details
Main Authors: Buchstaber, V. M. (Author), Panov, Taras E., 1975- (Author)
Corporate Author: American Mathematical Society (Publisher)
Language:English
Published: Providence, Rhode Island : American Mathematical Society, [2015]
Series:Mathematical surveys and monographs ; v. 204.
Subjects:
Toric varieties.
Algebraic varieties.
Algebraic topology.
Geometry, Algebraic.
Commutative algebra > Arithmetic rings and other special rings > Stanley-Reisner face rings; simplicial complexes.
Algebraic geometry > Special varieties > Toric varieties, Newton polyhedra.
Several complex variables and analytic spaces > Complex manifolds > Topological aspects of complex manifolds.
Convex and discrete geometry > Polytopes and polyhedra > Combinatorial properties (number of faces, shortest paths, etc.)
Algebraic topology > Homology and cohomology theories > Bordism and cobordism theories, formal group laws.
Algebraic topology > Homology and cohomology theories > Equivariant homology and cohomology.
Algebraic topology > Homotopy groups > Whitehead products and generalizations.
Manifolds and cell complexes > Differential topology > Equivariant cobordism.
Manifolds and cell complexes > Differential topology > Equivariant algebraic topology of manifolds.
Physical Description:xiii, 518 pages : illustrations ; 27 cm.
Format: Book
Contents:
  • Geometry and combinatorics of polytopes
  • Combinatorial structures
  • Combinatorial algebra of face rings
  • Moment-angle complexes
  • Toric varieties and manifolds
  • Geometric structures on moment-angle manifolds
  • Half-dimensional torus actions
  • Homotopy theory of polyhedral products
  • Torus actions and complex cobordism
  • Appendix A. Commutative and homological algebra
  • Appendix B. Algebraic topology
  • Appendix C. Categorial constructions
  • Appendix D. Bordism and cobordism
  • Appendix E. Formal group laws and Hirzebruch genera.