DOI

10.17077/etd.js8siee4

Document Type

Dissertation

Date of Degree

Spring 2010

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mathematics

First Advisor

Frohman, Charles

Second Advisor

Randell, Richard

First Committee Member

Durumeric, Oguz

Second Committee Member

Tomova, Madlena

Third Committee Member

Hunnicutt, Benjamin

Abstract

Mikhail Khovanov developed a bi-graded homology theory for links in the 3-sphere. Khovanov's theory came from a Topological quantum field theory (TQFT) and as such has a geometric interpretation, explored by Dror Bar-Natan. Marta Asaeda, Jozef Przytycki and Adam Sikora extended Khovanov's theory to I-bundles using decorated diagrams. Their theory did not suggest an obvious geometric version since it was not associated to a TQFT. We develop a geometric version of Asaeda, Przytycki and Sikora's theory for links in thickened surfaces. This version leads to two other distinct theories that we also explore.

Keywords

homology, knots, links, thickened surface

Pages

x, 93 pages

Bibliography

Includes bibliographical references (page 93).

Copyright

Copyright 2010 Jeffrey Thomas Conley Boerner

Included in

Mathematics Commons

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