2007/06/30 by Lawrence P. Roberts, Lawrence Roberts · 32 citations
Mathematics · #Advanced Combinatorial Mathematics #Floer homology #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Khovanov homology #Knot (papermaking) #Knot complement #Knot invariant #Locus (genetics) #Spectral sequence #Unknot #math.GT
paper · pdf · doi:10.2140/gt.2013.17.413
published in Geometry & Topology 17(1), 413-467 (Mathematical Sciences Publishers) · Due to an error in section 8, the results on the contact element have been weakened
arxiv created 2008/02/13 · openalex publication_date 2013/03/12 · arxiv updated 2014/11/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We define a link surgery spectral sequence for each knot Floer homology group for a knot, K , in a three manifold, Y . When K arises as the double cover of an unknot in S 3 , and Y is the double cover of S 3 branched over a link, we relate the E 2 -page to a version of Khovanov homology for links in an annulus defined by Asaeda, Przytycki and Sikora. Finally we examine the specific cases when the branch locus is a braid, and when it is alternating.