Instantons, Bar-Natan homology, and some concordance invariants of knots

P. B. Kronheimer; T. S. Mrowka

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arXiv · 1905.00828

Instantons, Bar-Natan homology, and some concordance invariants of knots

P. B. Kronheimer·T. S. Mrowka

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Abstract

A spectral sequence is established, from Bar-Natan's variant of Khovanov homology to a deformation of instanton homology for knots and links. This spectral sequence arises as a specialization of a spectral sequence from a characteristic-2 version of $F_5$ homology, in Khovanov'sclassification. Concordance invariants of knots are derived from the corresponding instanton homology groups, including a 1-parameter family of homomorphisms $f_r$ from the concordance group to the reals, having the potential to provide independent bounds on the genus and number of double points for immersed surfaces with boundary a given knot.

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BibTeX RIS

P. B. Kronheimer, T. S. Mrowka. 2019-05-02. Instantons, Bar-Natan homology, and some concordance invariants of knots. https://arxiv.org/abs/1905.00828

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