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arXiv · 2307.11461

Bar-Natan Homology for null homologous links in \mathbb{RP}^3

Daren Chen
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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.

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Daren Chen. 2023-07-21. Bar-Natan Homology for null homologous links in \mathbb{RP}^3. https://doi.org/10.2140/pjm.2025.334.233

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