Bar-Natan Homology for null homologous links in \mathbb{RP}^3
arXiv:2307.11461 · doi:10.2140/pjm.2025.334.233
Abstract
In this paper, we introduce Bar-Natan homology for null homologous links in \mathbb{RP}^3 over the field of two elements. It is a deformation of the Khovanov homology in \mathbb{RP}^3 defined by Asaeda, Przytycki and Sikora. We also define an s-invariant from this deformation using the same recipe as for links in S^3, and prove some genus bound using it. The key ingredient is the notion of twisted orientation for null homologous links and cobordisms in \mathbb{RP}^3.
29 pages, 21 figures. Comments are welcome