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Index Theory

Disselhorst, L.J. (2012) Index Theory. Bachelor's Thesis, Mathematics.

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Is it possible to comb the hairs of a billiard ball? In other words, can a singularity-free vector field exist on the 2-sphere? This is a question that can be answered using index theory. First, the definition of an index is discussed, after which we will prove that a vector field on the sphere must have singularities and that the sum of indices is independent of the vector field on the sphere. Finally, we will consider other manifolds, both homeomorphic and not homeomorphic to the sphere.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 07:49
Last Modified: 15 Feb 2018 07:50

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