On the colored Jones polynomial, sutured Floer homology, and knot Floer homology |
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Authors: | J Elisenda Grigsby Stephan M Wehrli |
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Institution: | a Boston College, Department of Mathematics, 301 Carney Hall, Chestnut Hill, MA 02467, United States b Columbia Math. Dept., 2990 Broadway MC4406, New York, NY 10027, United States |
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Abstract: | Let K⊂S3, and let denote the preimage of K inside its double branched cover, Σ(S3,K). We prove, for each integer n>1, the existence of a spectral sequence whose E2 term is Khovanov's categorification of the reduced n-colored Jones polynomial of (mirror of K) and whose E∞ term is the knot Floer homology of (when n odd) and of (S3,K#Kr) (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. |
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Keywords: | Link invariants Floer homology Khovanov homology Colored Jones polynomial Sutured manifolds Unknot detection |
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