Khovanov homology is an unknot-detector

P. B. Kronheimer; T. S. Mrowka

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arXiv · 1005.4346

Khovanov homology is an unknot-detector

P. B. Kronheimer·T. S. Mrowka

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Abstract

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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P. B. Kronheimer, T. S. Mrowka. 2010-05-24. Khovanov homology is an unknot-detector. https://arxiv.org/abs/1005.4346

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