English

A module structure on odd Khovanov homology and the odd invariant for ribbon 2-knots

Geometric Topology 2026-07-04 v1

Abstract

We prove that the reduced odd Khovanov homology of a link LL is naturally a module over the exterior algebra of the first homology of the link's branched double-cover. We then describe this module structure more geometrically and related it to the odd Khovanov maps induced by link cobordisms. As an application, we will give a combinatorial proof of a recent result of Spyropoulos-Vidyarthi-Zhang about the odd invariant for 22-knots in the special case where the 22-knot is a ribbon 22-knot. Additionally, we will show that Levine-Zemke's main result from their 2019 paper on Khovanov homology and ribbon concordance remains true for odd Khovanov homology with rational coefficients and with coefficients in Z2k\mathbb{Z}_{2^k}.

Keywords

Cite

@article{arxiv.2607.04018,
  title  = {A module structure on odd Khovanov homology and the odd invariant for ribbon 2-knots},
  author = {Jacob Migdail and Stephan Wehrli},
  journal= {arXiv preprint arXiv:2607.04018},
  year   = {2026}
}

Comments

55 pages, many figures