Date of Degree

2010

Document Type

PhD diss.

Degree Name

PhD (Doctor of Philosophy)

Department

Mathematics

First Advisor

Charles Frohman

Abstract

A homology theory is defined for equivalence classes of links under isotopy in the 3-sphere. Chain modules for a link L are generated by certain surfaces whose boundary is L, using surface signature as the homological grading. In the end, the diagramless homology of a link is found to be equal to some number of copies of the Khovanov homology of that link. There is also a discussion of how one would generalize the diagramless homology theory (hence the theory of Khovanov homology) to links in arbitrary closed oriented 3-manifolds.

Pages

viii, 80

Bibliography

79-80

Copyright

Copyright 2010 Adam Corey McDougall

Included in

Mathematics Commons

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