Khovanov-type homologies of null homologous links in $\mathbb{RP}^3$

Daren Chen

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arXiv · 2104.04779

Khovanov-type homologies of null homologous links in $\mathbb{RP}^3$

Daren Chen

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Abstract

Let L be a null homologous link in $\mathbb{RP}^3$. We define Khovanov-type homologies of L which depend on an extra input $\alpha = (V_0,V_1,f,g)$ consisting of two graded vectors spaces and two maps between them. With some specific choice of $\alpha = \alpha_{APS}$, we recover the categorification of the Kauffman bracket due to Asaeda-Przytycki-Sikora. With another choice of $\alpha = \alpha_{HF}$, we construct a spectral sequence from our theory converging to the Heegaard Floer homology of the even branched double cover of $\mathbb{RP}^3$.

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Daren Chen. 2021-04-10. Khovanov-type homologies of null homologous links in $\mathbb{RP}^3$. https://arxiv.org/abs/2104.04779

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