Khovanov homology is an unknot-detector

Details Khovanov homology is an unknot-detector Khovanov homology is an unknot-detector

2010-05-24

arxiv.org/abs/1005.4346v1

Mathematics

Geometric Topology

124 pages, 13 figures

Scientific paper

We prove that a knot is the unknot if and only if its reduced Khovanov cohomology has rank 1. The proof has two steps. We show first that there is a spectral sequence beginning with the reduced Khovanov cohomology and abutting to a knot homology defined using singular instantons. We then show that the latter homology is isomorphic to the instanton Floer homology of the sutured knot complement: an invariant that is already known to detect the unknot.

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