DOI

10.17077/etd.q5td-f3q0

Document Type

Dissertation

Date of Degree

Summer 2019

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mathematics

First Advisor

Cooper, Benjamin

First Committee Member

Frohman, Charles

Second Committee Member

Mitchell, Colleen

Third Committee Member

Tehrani, Mohammad

Fourth Committee Member

Darcy, Isabel

Abstract

We prove an equivalence between the category underlying combinatorial tangle Floer homology and the contact category by building on the prior work of Lipshitz, Ozsváth, and Thurston and later Zhan. In his 2015 paper "Formal Contact Categories", Cooper establishes a relationship between the categories associated to oriented surfaces by Heegaard Floer theory and embedded contact theory. In this thesis, we examine a special case of his general argument to show an equivalence between the categories discussed by Petkova and Vértesi and those discussed by Tian. To do this, we construct two bimodules associated to the transformations between the underlying structure of combinatorial tangle Floer homology and the contact category. We take the tensor product of these bimodules and show that the product is equivalent to the identity, inducing an isomorphism between the categories of interest.

Pages

x, 112 pages

Bibliography

Includes bibliographical references (page 112).

Copyright

Copyright © 2019 Rebeccah MacKinnon

Included in

Mathematics Commons

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