Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry - Brossura

Matousek, Jiri

 
9783540003625: Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry
Brossura
ISBN 10: 3540003622 ISBN 13: 9783540003625
Casa editrice: Springer Berlin Heidelberg, 2008

Sinossi

<p>To the uninitiated, algebraic topology might seem fiendishly complex, but its utility is beyond doubt. This brilliant exposition goes back to basics to explain how the subject has been used to further our understanding in some key areas. A number of important results in combinatorics, discrete geometry, and theoretical computer science have been proved using algebraic topology. While the results are quite famous, their proofs are not so widely understood. This book is the first textbook treatment of a significant part of these results. It focuses on so-called equivariant methods, based on the Borsuk-Ulam theorem and its generalizations. The topological tools are intentionally kept on a very elementary level. No prior knowledge of algebraic topology is assumed, only a background in undergraduate mathematics, and the required topological notions and results are gradually explained.</p>

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Dalla quarta di copertina

<p>"The "Kneser conjecture" -- posed by Martin Kneser in 1955 in the Jahresbericht der DMV -- is an innocent-looking problem about partitioning the k-subsets of an n-set into intersecting subfamilies. Its striking solution by L. Lovász featured an unexpected use of the Borsuk-Ulam theorem, that is, of a genuinely topological result about continuous antipodal maps of spheres. </p><p></p><p>Matousek's lively little textbook now shows that Lovász' insight as well as beautiful work of many others (such as Vrecica and Zivaljevic, and Sarkaria) have opened up an exciting area of mathematics that connects combinatorics, graph theory, algebraic topology and discrete geometry. What seemed like an ingenious trick in 1978 now presents itself as an instance of the "test set paradigm": to construct configuration spaces for combinatorial problems such that coloring, incidence or transversal problems may be translated into the (non-)existence of suitable equivariant maps. </p><p></p><p>The vivid account of this area and its ramifications by Matousek is an exciting, a coherent account of this area of topological combinatorics. It features a collection of mathematical gems written with a broad view of the subject and still with loving care for details. Recommended reading! […]"</p><p></p><p><em>Günter M.Ziegler (Berlin)</em><br>Zbl. MATH Volume 1060 Productions-no.: 05001</p><p></p>

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

Editore
Springer Berlin Heidelberg
Data di pubblicazione
2008
Lingua
Inglese
ISBN 10 
3540003622
ISBN 13 
9783540003625
Rilegatura
Copertina flessibile
Numero di pagine
226
Contatto del produttore
non disponibile
Persona responsabile
CMN Printpool Inh. Mathis Neumann
https://www.also.com/ec/cms5/en_6000/6000/index.jsp

Friedrich-Karl-Str. 9
Hamburg
Germania

Altre edizioni note dello stesso titolo

9783662308660: Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry

Edizione in evidenza

ISBN 10:  3662308665 ISBN 13:  9783662308660
Casa editrice: Springer, 2014
Brossura