The Resource Toric topology, Victor M. Buchstaber, Taras E. Panov

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

Label
Toric topology
Title
Toric topology
Statement of responsibility
Victor M. Buchstaber, Taras E. Panov
Creator
Contributor
Author
Publisher
Subject
Language
eng
Summary
"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
Member of
Cataloging source
DLC
http://library.link/vocab/creatorName
Buchstaber, V. M
Dewey number
516.3/5
Illustrations
illustrations
Index
index present
LC call number
QA613.2
LC item number
.B82 2015
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1975-
http://library.link/vocab/relatedWorkOrContributorName
  • Panov, Taras E.
  • American Mathematical Society
Series statement
Mathematical surveys and monographs
Series volume
volume 204
http://library.link/vocab/subjectName
  • 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
  • Algebraic topology
  • Algebraic varieties
  • Geometry, Algebraic
  • Toric varieties
Label
Toric topology, Victor M. Buchstaber, Taras E. Panov
Instantiates
Publication
Copyright
Bibliography note
Includes bibliographical references (pages 495-509) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Dimensions
27 cm.
Extent
xiii, 518 pages
Isbn
9781470422141
Lccn
2015006771
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
  • (OCoLC)904011926
  • (OCoLC)ocn904011926
Label
Toric topology, Victor M. Buchstaber, Taras E. Panov
Publication
Copyright
Bibliography note
Includes bibliographical references (pages 495-509) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Dimensions
27 cm.
Extent
xiii, 518 pages
Isbn
9781470422141
Lccn
2015006771
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
  • (OCoLC)904011926
  • (OCoLC)ocn904011926

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