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

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.

This paper has been withdrawn as its content is superseded by two more recent papers. The newer papers are arXiv:1910.11128 and arXiv:1910.11129, which separately treat the previous material relating instanton homology to Bar-Natan homology, and concordance invariants respectively

References in corpus (2)

• Concordance homomorphisms from knot Floer homology
• Gauge theory and Rasmussen's invariant

Cited by in corpus (1)

• Chern-Simons functional, singular instantons, and the four-dimensional clasp number