Year of Publication

2016

Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation

College

Arts and Sciences

Department

Mathematics

First Advisor

Dr. Serge Ochanine

Abstract

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.

Digital Object Identifier (DOI)

http://dx.doi.org/10.13023/ETD.2016.282

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