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 language | English (US) |
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Pages (from-to) | 2114-2165 |
Number of pages | 52 |
Journal | Advances in Mathematics |
Volume | 223 |
Issue number | 6 |
DOIs | |
State | Published - Apr 1 2010 |
Externally published | Yes |
Keywords
- Colored Jones polynomial
- Floer homology
- Khovanov homology
- Link invariants
- Sutured manifolds
- Unknot detection
ASJC Scopus subject areas
- General Mathematics