An unoriented skein exact triangle for knot Floer homology

Given a crossing in a planar diagram of a link in the three-sphere, we show that the knot Floer homologies of the link and its two resolutions at that crossing are related by an exact triangle. As a consequence, we deduce that for any quasi-alternating link, the total rank of its knot Floer homology is equal to the determinant of the link.

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Published 1 January 2007