Khovanov-type homologies of null homologous links in $\mathbb{RP}^{3}$
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_{\mathrm{APS}} , we recover the categorification of the Kauffman bracket due to Asaeda–Przytycki–Sikora. With another choice of \alpha = \alpha_{\mathrm{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} .
Fields of Study & Subjects
Geometric and Algebraic Topology
Homotopy and Cohomology in Algebraic Topology
Topological and Geometric Data Analysis
Publication details
- Journal / source
- Quantum Topology
- Volume
- 17
- Issue
- 3
- Pages
- 467–508
- Publication date
- 14 April 2026
- Language
- EN