In algebraic topology, we work to classify objects. My research aims to build a better understanding of one important notion of classification of differentiable manifolds called cobordism. Cobordism is an equivalence relation, and the equivalence classes in cobordism form a graded ring, with operations disjoint union and Cartesian product. My dissertation studies this graded ring in two ways:
1. by attempting to find preferred class representatives for each class in the ring.
2. by computing the image of the ring under an interesting ring homomorphism called the Witten Genus.
| Identifer | oai:union.ndltd.org:uky.edu/oai:uknowledge.uky.edu:math_etds-1036 |
| Date | 01 January 2016 |
| Creators | Mosley, John E. |
| Publisher | UKnowledge |
| Source Sets | University of Kentucky |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Theses and Dissertations--Mathematics |
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