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Torus Actions and Their Applications in Topology and Combinatorics download ebook

by Victor M. Buchstaber and Taras E. Panov

Torus Actions and Their Applications in Topology and Combinatorics download ebook
ISBN:
0821831860
ISBN13:
978-0821831861
Author:
Victor M. Buchstaber and Taras E. Panov
Publisher:
American Mathematical Society (May 1, 2002)
Language:
ePUB:
1792 kb
Fb2:
1301 kb
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Category:
Mathematics
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Rating:
4.6

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

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. 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.

Victor M. Buchstaber Taras E. Panov. American Mathematical Society. Mathematical Surveys and Monographs Volume 204. Toric Topology Victor M. American Mathematical Society Providence, Rhode Island. The title ‘Toric Topology’ coined by our colleague Nigel Ray became official after the 2006 Osaka conference under the same name. Buchstaber and Taras E. Torus Actions and Their Applications in Topology and Combinatorics. A toric topology section within the International Conference & Equations and Topology'', . Pontrjagin Centenary (Moscow, June 2008). University Lecture Series, vo. 4, American Mathematical Society, Providence, RI, 2002 (152 pages). pdf (preprint version). Conferences and meetings in toric topology include. International Conference & Horizons in Toric Topology'' (Manchester, .

Victor Matveevich Buchstaber, Taras E. Here, 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. Conversely, subtle properties of a combinatorial object can be realized by interpreting it as the orbit structure for a proper manifold or as . ONTINUE READING.

Author Buchstaber, V. Buchstaber, Victor . Buchstaber, V M, Panov, Taras E. ISBN 0821831860. ISBN13: 9780821831861. More Books . ABOUT CHEGG.

Электронная книга "Torus Actions and Their Applications in Topology and Combinatorics", V. M. Buchstaber, Taras E. Panov

Электронная книга "Torus Actions and Their Applications in Topology and Combinatorics", V. Эту книгу можно прочитать в Google Play Книгах на компьютере, а также на устройствах Android и iOS. Выделяйте текст, добавляйте закладки и делайте заметки, скачав книгу "Torus Actions and Their Applications in Topology and Combinatorics" для чтения в офлайн-режиме. 22 2. topology and combinatorics of simplicial complexes. Department of Mathematics and Mechanics, Moscow State Univer-sity, 119899 Moscow RUSSIA. Torus actions on topological spaces is a classical and one of the most developed elds in the equivariant topology. Specic problems connected with torus actions arise in dierent areas of mathematics and mathematical physics, which results in the permanent interest to the theory, constant source of new applications and penetration of new ideas in topology. b) the intersection of any two simplices in U is a face of each. Buchstaber; Taras E. The corresponding quotient is a smooth manifold Z P invested with a canonical action of the compact torus T^m with the orbit space P^n. For each smooth projective toric variety M^{2n} defined by a simple polytope P^n with the given lattice of faces there exists a subgroup T^{m-n}subset T^m acting freely on Z P. such that Z P/T^{m-n} M^{2n}. We calculate the cohomology ring of Z P and show that it is isomorphic to the cohomology ring of the face ring of P^n regarded as a module over the polynomial ring.

M. Buchstaber and T. E. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 75th birthday, Tr. Mat. Inst. Torus actions and their applications in topology and combinatorics // AMS University Lectures Series 24, American Mathematical Society, Providence, RI, 2002. List of publications on Google Scholar. org/authors/?q ai:panov.

Torus Actions and their Applications in Topology and Combinatorics We present a beautiful interplay between combinatorial topology and homological algebra for a class of monoids that arise naturally.

Torus Actions and their Applications in Topology and Combinatorics. Victor Matveevich Buchstaber. 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. We present a beautiful interplay between combinatorial topology and homological algebra for a class of monoids that arise naturally in algebraic combinatorics. We explore several applications of this interplay.

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.