An algebraic proof of invariance for knot Floer homology

Details An algebraic proof of invariance for knot Floer homology An algebraic proof of invariance for knot Floer homology

2010-07-15

arxiv.org/abs/1007.2609v1

Mathematics

Geometric Topology

36 pages, 19 figures

Scientific paper

We present a proof of the invariance of knot Floer homology using the cube of resolutions construction first described by Ozsvath and Szabo. Specifically, we show that the cube of resolutions chain complex is invariant up to chain homotopy equivalence and base change under the Markov moves. The techniques echo those employed by Khovanov and Rozansky to prove the invariance of HOMFLY-PT homology. In particular, we make no mention of holomorphic disks or grid diagrams.

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