Document Type

Article

Date

10-5-2008

Embargo Period

11-18-2011

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.

Additional Information

This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/0810.0778

Source

Harvested from arXiv.org

Included in

Mathematics Commons

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