The Borsuk-Ulam Theorem in Combinatorics

Bachelor Thesis (2017)
Author(s)

I.J. Jaspers (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Contributor(s)

D.C. Gijswijt – Mentor

KP Hart – Graduation committee member

J.G. Spandaw – Graduation committee member

Faculty
Electrical Engineering, Mathematics and Computer Science
Copyright
© 2017 Ilja Jaspers
More Info
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Publication Year
2017
Language
English
Copyright
© 2017 Ilja Jaspers
Graduation Date
23-08-2017
Awarding Institution
Delft University of Technology
Faculty
Electrical Engineering, Mathematics and Computer Science
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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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