Using the Borsuk-Ulam theorem : lectures on topological methods in combinatorics and geometry

Jiří Matoušek ; written in cooperation with Anders Björner and Günter M. Ziegler

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.

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[目次]

  • Simplicial Complexes.- The Borsuk-Ulam Theorem.- Direct Applications of Borsuk-Ulam.- A Topological Interlude.- ?2-Maps and Nonembeddability.- Multiple Points of Coincidence.

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この本の情報

書名 Using the Borsuk-Ulam theorem : lectures on topological methods in combinatorics and geometry
著作者等 Björner, Anders
Matoušek, Jiří
Ziegler, Gunter M
Bjorner Anders
Ziegler G.M.
Matousek Jiri
シリーズ名 Universitext
出版元 Springer
刊行年月 2008
版表示 2nd, corr. printing
ページ数 xii, 210 p.
大きさ 24 cm
ISBN 9783540003625
NCID BA84830401
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言語 英語
出版国 ドイツ
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