Date of Degree
2010
Document Type
dissertation
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
Recommended Citation
Boerner, Jeffrey Thomas Conley. "Khovanov homology in thickened surfaces." dissertation, University of Iowa, 2010.
http://ir.uiowa.edu/etd/464.