Towards a symplectic Khovanov homology for links in fibered $3$-manifolds
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912678186844160 |
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| author | Colin, Vincent Honda, Ko Tian, Yin |
| author_facet | Colin, Vincent Honda, Ko Tian, Yin |
| contents | 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-Ozsváth-Thurston \cite{LOT}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26164 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards a symplectic Khovanov homology for links in fibered $3$-manifolds Colin, Vincent Honda, Ko Tian, Yin Symplectic Geometry Geometric Topology Quantum Algebra 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-Ozsváth-Thurston \cite{LOT}. |
| title | Towards a symplectic Khovanov homology for links in fibered $3$-manifolds |
| topic | Symplectic Geometry Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2510.26164 |