On the colored Jones polynomial, sutured Floer homology, and knot Floer homology

J. Elisenda Grigsby, Stephan M. Wehrli

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

Let K ⊂ S3, and let over(K, ̃) 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 over(K, -) (mirror of K) and whose E term is the knot Floer homology of (Σ (S3, K), over(K, ̃)) (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.

Original languageEnglish (US)
Pages (from-to)2114-2165
Number of pages52
JournalAdvances in Mathematics
Volume223
Issue number6
DOIs
StatePublished - Apr 1 2010
Externally publishedYes

Keywords

  • Colored Jones polynomial
  • Floer homology
  • Khovanov homology
  • Link invariants
  • Sutured manifolds
  • Unknot detection

ASJC Scopus subject areas

  • Mathematics(all)

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