# On the Colored Jones Polynomial, Sutured Floer homology, and Knot Floer homology

@article{Grigsby2008OnTC, title={On the Colored Jones Polynomial, Sutured Floer homology, and Knot Floer homology}, author={Julia Elisenda Grigsby and Stephan Martin Wehrli}, journal={arXiv: Geometric Topology}, year={2008} }

Let K in S^3 be a knot, and let \widetilde{K} denote the preimage of K inside its double branched cover, \Sigma(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 the mirror of K to the knot Floer homology of (\Sigma(K),\widetilde{K}) (when n odd) and to (S^3, K # K) (when n even). A corollary of our result is that Khovanov's categorification of the reduced n-colored Jones polynomial detects…

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