2008/07/09 by J. Elisenda Grigsby, Grigsby, J. Elisenda, Stephan M. Wehrli +2
Mathematics · #57M12 #57M27 #57R58 #81R50 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG) #math.GT #math.QA #math.SG #msc:57M12 #msc:57M27 #msc:57R58 #msc:81R50
paper · pdf · doi:10.48550/arxiv.0807.1432
46 pages, 13 figures; Unnecessary assumptions in statement of link surgeries spectral sequence (Section 4) removed, references updated, minor typos corrected throughout
openalex publication_date 2008/07/09 · arxiv created 2008/10/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Let K in S3 be a knot, and let \widetildeK denote the preimage of K inside its double branched cover, Σ(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 (Σ(K),\widetildeK) (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.