Klein, R (2013) Swan's Theorem. Bachelor's Thesis, Mathematics.
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Abstract
In this thesis we examine Swan's theorem, which states that that given a compact Hausdorff space X, any finitely generated projective module over the continuous functions on X is isomorphic to the module of sections of a topological vector bundle over X. Conversely it states that any module of sections of a topological vector bundle over X is a finitely generated and projective module over the continuous functions on X. After covering some preliminaries concerning vector bundles and projective modules we examine vector bundles over compact Hausdorff spaces and subsequently give the proof of Swan's theorem. We also examine the scope of Swan's theorem and consider a generalization due to Vaserstein.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 15 Feb 2018 07:52 |
| Last Modified: | 15 Feb 2018 07:52 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/10888 |
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