Document Type
Article
Date
10-5-2008
Disciplines
Mathematics
Description/Abstract
Khovanov homology ist a new link invariant, discovered by M. Khovanov, and used by J. Rasmussen to give a combinatorial proof of the Milnor conjecture. In this thesis, we give examples of mutant links with different Khovanov homology. We prove that Khovanov's chain complex retracts to a subcomplex, whose generators are related to spanning trees of the Tait graph, and we exploit this result to investigate the structure of Khovanov homology for alternating knots. Further, we extend Rasmussen's invariant to links. Finally, we generalize Khovanov's categorifications of the colored Jones polynomial, and study conditions under which our categorifications are functorial with respect to colored framed link cobordisms. In this context, we develop a theory of Carter-Saito movie moves for framed link cobordisms.
Recommended Citation
Wehrli, Stephan M., "Contributions to Khovanov Homology" (2008). Mathematics - All Scholarship. 116.
https://surface.syr.edu/mat/116
Source
Harvested from arXiv.org
Additional Information
This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/0810.0778