An unoriented skein exact triangle for knot Floer homology

Details An unoriented skein exact triangle for knot Floer homology An unoriented skein exact triangle for knot Floer homology

2006-09-19

arxiv.org/abs/math/0609531v3

Math. Res. Lett. 14 (2007), 839--852

Mathematics

Geometric Topology

13 pages, 10 figures; 9_46 dropped from the list of quasi-alternating knots

Scientific paper

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 knot, the total rank of its knot Floer homology is equal
to the determinant of the knot.

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