Using the Borsuk-Ulam Theorem

Using the Borsuk-Ulam Theorem

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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.The first steps can be made with Munkres [Mun00] (which includes preparation in general topology) or Stillwell [Sti93]. A very ... For patient answers to my numerous questions I am much indebted to Rade EĀ‡Zivaljevic and Imre BAirAiny. Specialanbsp;...

Title:Using the Borsuk-Ulam Theorem
Author: Jiri Matousek
Publisher:Springer Science & Business Media - 2008-01-12

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