Date of Degree
2010
Document Type
dissertation
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
Recommended Citation
McDougall, Adam Corey. "Relating Khovanov homology to a diagramless homology." dissertation, University of Iowa, 2010.
http://ir.uiowa.edu/etd/709.