On the Khovanov and knot Floer homologies of quasi-alternating links
arXiv:0708.3249
Abstract
Quasi-alternating links are a natural generalization of alternating links. In this paper, we show that quasi-alternating links are "homologically thin" for both Khovanov homology and knot Floer homology. In particular, their bigraded homology groups are determined by the signature of the link, together with the Euler characteristic of the respective homology (i.e. the Jones or the Alexander polynomial). The proofs use the exact triangles relating the homology of a link with the homologies of its two resolutions at a crossing.
19 pages, 13 figures; minor revisions; to appear in Proceedings of the 14th Gokova Geometry / Topology Conference