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arXiv · 2510.26164

Towards a symplectic Khovanov homology for links in fibered $3$-manifolds

Vincent Colin·Ko Honda·Yin Tian
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Abstract

The goal of this paper is twofold: (i) define a symplectic Khovanov type homology for a transverse link in a fibered closed $3$-manifold $M$ (with an auxiliary choice of a homotopy class of loops that intersect each fiber once) and (ii) give conjectural combinatorial dga descriptions of surface categories that appear in (i). These dgas are higher-dimensional analogs of the strands algebras in bordered Heegaard Floer homology, due to Lipshitz-Ozsv\'ath-Thurston \cite{LOT}.

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BibTeXRIS

Vincent Colin, Ko Honda, Yin Tian. 2025-10-30. Towards a symplectic Khovanov homology for links in fibered $3$-manifolds. https://arxiv.org/abs/2510.26164

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