Document Type
Article
Date
10-13-2008
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.
Recommended Citation
Grigsby, J. Elisenda and Wehrli, Stephan, "On the Colored Jones Polynomial, Sutured Floer Homology, and Knot Floer Homology" (2008). Mathematics - All Scholarship. 115.
https://surface.syr.edu/mat/115
Source
Harvested from arXiv.org
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Additional Information
This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/0807.1432