Document Type

PhD diss.

Date of Degree

2010

Degree Name

PhD (Doctor of Philosophy)

Department

Mathematics

First Advisor

Charles Frohman

Second Advisor

Richard Randell

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.

Pages

x, 93

Bibliography

93

Copyright

Copyright 2010 Jeffrey Thomas Conley Boerner

Included in

Mathematics Commons

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