The problem of embedding a manifold in Euclidean space is considered. Manifolds are introduced in Chapter I along with other basic definitions and examples. Chapter II contains a proof of the Regular Value Theorem along with the "Easy" Whitney Embedding Theorem. In Chapter III, vector bundles are introduced and some of their properties are discussed. Chapter IV introduces the Stiefel-Whitney classes and the four properties that characterize them. Finally, in Chapter V, the Stiefel-Whitney classes are used to produce a lower bound on the dimension of Euclidean space that is needed to embed real projective space.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc504181 |
| Date | 08 1900 |
| Creators | Green, Michael Douglas, 1965- |
| Contributors | Brand, Neal E., Curran, Stephen |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iii, 90 leaves : ill., Text |
| Rights | Public, Green, Michael Douglas, 1965-, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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