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Torus actions and their applications in topology and combinatorics
The book presents the study of torus actions on topological spaces is presented as a bridge connecting combinatorial and convex geometry with commutative and homological algebra, algebraic geometry, and topology. This established link helps in understanding the geometry and topology of a space with...
Autores principales: | , |
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Lenguaje: | eng |
Publicado: |
American Mathematical Society
2002
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Acceso en línea: | http://cds.cern.ch/record/2623115 |
_version_ | 1780958664338702336 |
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author | Buchstaber, Victor M Panov, Taras E |
author_facet | Buchstaber, Victor M Panov, Taras E |
author_sort | Buchstaber, Victor M |
collection | CERN |
description | The book presents the study of torus actions on topological spaces is presented as a bridge connecting combinatorial and convex geometry with commutative and homological algebra, algebraic geometry, and topology. This established link helps in understanding the geometry and topology of a space with torus action by studying the combinatorics of the space of orbits. Conversely, subtle properties of a combinatorial object can be realized by interpreting it as the orbit structure for a proper manifold or as a complex acted on by a torus. The latter can be a symplectic manifold with Hamiltonian torus action, a toric variety or manifold, a subspace arrangement complement, etc., while the combinatorial objects include simplicial and cubical complexes, polytopes, and arrangements. This approach also provides a natural topological interpretation in terms of torus actions of many constructions from commutative and homological algebra used in combinatorics. The exposition centers around the theory of moment-angle complexes, providing an effective way to study invariants of triangulations by methods of equivariant topology. The book includes many new and well-known open problems and would be suitable as a textbook. It will be useful for specialists both in topology and in combinatorics and will help to establish even tighter connections between the subjects involved. |
id | cern-2623115 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2002 |
publisher | American Mathematical Society |
record_format | invenio |
spelling | cern-26231152021-04-21T18:47:36Zhttp://cds.cern.ch/record/2623115engBuchstaber, Victor MPanov, Taras ETorus actions and their applications in topology and combinatoricsMathematical Physics and MathematicsThe book presents the study of torus actions on topological spaces is presented as a bridge connecting combinatorial and convex geometry with commutative and homological algebra, algebraic geometry, and topology. This established link helps in understanding the geometry and topology of a space with torus action by studying the combinatorics of the space of orbits. Conversely, subtle properties of a combinatorial object can be realized by interpreting it as the orbit structure for a proper manifold or as a complex acted on by a torus. The latter can be a symplectic manifold with Hamiltonian torus action, a toric variety or manifold, a subspace arrangement complement, etc., while the combinatorial objects include simplicial and cubical complexes, polytopes, and arrangements. This approach also provides a natural topological interpretation in terms of torus actions of many constructions from commutative and homological algebra used in combinatorics. The exposition centers around the theory of moment-angle complexes, providing an effective way to study invariants of triangulations by methods of equivariant topology. The book includes many new and well-known open problems and would be suitable as a textbook. It will be useful for specialists both in topology and in combinatorics and will help to establish even tighter connections between the subjects involved.American Mathematical Societyoai:cds.cern.ch:26231152002 |
spellingShingle | Mathematical Physics and Mathematics Buchstaber, Victor M Panov, Taras E Torus actions and their applications in topology and combinatorics |
title | Torus actions and their applications in topology and combinatorics |
title_full | Torus actions and their applications in topology and combinatorics |
title_fullStr | Torus actions and their applications in topology and combinatorics |
title_full_unstemmed | Torus actions and their applications in topology and combinatorics |
title_short | Torus actions and their applications in topology and combinatorics |
title_sort | torus actions and their applications in topology and combinatorics |
topic | Mathematical Physics and Mathematics |
url | http://cds.cern.ch/record/2623115 |
work_keys_str_mv | AT buchstabervictorm torusactionsandtheirapplicationsintopologyandcombinatorics AT panovtarase torusactionsandtheirapplicationsintopologyandcombinatorics |