Toric topology
By: Victor M. Buchstaber, Taras E. Panov
Contributors: Panov, Taras E., 1975-
Series: Mathematical surveys and monographs -- volume 204
Publisher: American Mathematical Society
Published: 2015
Place of publication: Providence, Rhode Island
Language: eng
Number of pages: 518
ISBN-13: 9781470422141
Subjects: Toric varieties; Convex and discrete geometry -- Polytopes and polyhedra -- Combinatorial properties (number of faces, shortest paths, etc.).; Several complex variables and analytic spaces -- Complex manifolds -- Topological aspects of complex manifolds; Algebraic Geometry; Algebraic varieties; Algebraic topology -- Homotopy groups -- Whitehead products and generalizations; Algebraic topology; Manifolds and cell complexes -- Differential topology -- Equivariant cobordism; Manifolds and cell complexes -- Differential topology -- Equivariant algebraic topology of manifolds; Algebraic topology -- Homology and cohomology theories -- Bordism and cobordism theories, formal group laws; Commutative algebra -- Arithmetic rings and other special rings -- Stanley-Reisner face rings; simplicial complexes; Algebraic geometry -- Special varieties -- Toric varieties, Newton polyhedra; Algebraic topology -- Homology and cohomology theories -- Equivariant homology and cohomology
Description: "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"--Back cover.
Notes: Includes bibliographical references (pages (495-509) and index.