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.
| Identifer | oai:union.ndltd.org:uiowa.edu/oai:ir.uiowa.edu:etd-1894 |
| Date | 01 July 2010 |
| Creators | McDougall, Adam Corey |
| Contributors | Frohman, Charles D. |
| Publisher | University of Iowa |
| Source Sets | University of Iowa |
| Language | English |
| Detected Language | English |
| Type | dissertation |
| Format | application/pdf |
| Source | Theses and Dissertations |
| Rights | Copyright 2010 Adam Corey McDougall |
Page generated in 0.0028 seconds