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Vector fields on spheres
Strakoš, Filip ; Salač, Tomáš (advisor) ; Golovko, Roman (referee)
This thesis deals with partial results concerning the problem of existence of vector fields on spheres. The proof of the Hairy Ball Theorem is given using the tools of the the- ory of characteristic classes. Basic notions of algebraic topology are stated in order to define the Euler class. Its definition is followed by the computation of the Euler charac- teristic class for the tangent bundle of even-dimensional sphere. In the rest of the text, the method of construction of vector fields on spheres using the orthogonal multiplica- tion is explained and the Radon-Hurwitz-Eckmann Theorem is proved. A brief historical background of the existence of the finite-dimensional real division algebras is mentioned at the end.
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