Document Type

Dissertation

Date of Degree

Summer 2010

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mathematics

First Advisor

Charles Frohman

First Committee Member

Charles Frohman

Second Committee Member

Dennis Roseman

Third Committee Member

Julianna Tymoczko

Fourth Committee Member

Fred Goodman

Fifth Committee Member

Dan Anderson

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.

Keywords

3-manifolds, diagramless, khovanov homology, knot theory, link homology, state surfaces

Pages

viii, 80 pages

Bibliography

Includes bibliographical references (pages 79-80).

Copyright

Copyright 2010 Adam Corey McDougall

Included in

Mathematics Commons

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