On knot Floer homology in double branched covers

Roberts, Lawrence¹

¹ Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA

Geometry & topology, Tome 17 (2013) no. 1, pp. 413-467.

Résumé

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.

Détail

DOI : 10.2140/gt.2013.17.413

Keywords: knot Floer homology, Khovanov homology, branched double cover

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