The Borsuk-Ulam Theorem in Combinatorics

Bachelor thesis (2017)

Authors

I.J. Jaspers Electrical Engineering, Mathematics and Computer Science

Contributors

Dion Gijswijt (mentor)
K.P. Hart (graduation committee member)
J.G. Spandaw (graduation committee member)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2017 Ilja Jaspers
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Published Date

23-08-2017

Language

English

Reuse Rights

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

We examine and prove the Borsuk-Ulam theorem and its combinatorial equivalent Fan's lemma. The theory of simplicial complexes and triangulations plays an important role in this. The Borsuk-Ulam theorem and Fan's lemma will be used to provide proofs for the Brouwer fixed point theorem and the combinatorial Sperner's lemma. Lastly the Borsuk-Ulam theorem will be applied in determining the chromatic number of Kneser graphs.

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