Document Type

Article

Date

10-13-2008

Embargo Period

11-18-2011

Disciplines

Mathematics

Description/Abstract

Let K in S3 be a knot, and let K denote the preimage of K inside its double branched cover, Sigma(S3, K). We prove, for each integer n > 1, the existence of a spectral sequence from Khovanov's categorification of the reduced n-colored Jones polynomial of K (mirror of K) and whose Einfinity term is the knot Floer homology of (Sigma(S3,K),K) (when n odd) and to (S3, K # K) (when n even). A corollary of our result is that Khovanov's categorification of the reduced n-colored Jones polynomial detects the unknot whenever n>1.

Additional Information

This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/0807.1432

Source

Harvested from arXiv.org

Creative Commons License

Creative Commons Attribution 3.0 License
This work is licensed under a Creative Commons Attribution 3.0 License.

Included in

Mathematics Commons

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