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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2506.04222 |
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| _version_ | 1866912413187571712 |
|---|---|
| author | Sethi, Shikhin |
| author_facet | Sethi, Shikhin |
| contents | Lipshitz, Ozsváth, and Thurston extend the theory of bordered Heegaard Floer homology to compute $\mathbf{CF}^-$. Like with the hat theory, their minus invariants provide a recipe to compute knot invariants associated to satellite knots. We combinatorially construct the weighted $A_\infty$-modules associated to the $(p, 1)$-cable. The operations on these modules count certain classes of inductively constructed decorated planar graphs. This description of the weighted $A_\infty$-modules provides a combinatorial proof of the $A_\infty$ structure relations for the modules. We further prove a uniqueness property for the modules we construct: any weighted extensions of the unweighted $U = 0$ modules have isomorphic associated type D modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04222 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bordered Heegaard Floer modules for satellite operations using planar graphs Sethi, Shikhin Geometric Topology Lipshitz, Ozsváth, and Thurston extend the theory of bordered Heegaard Floer homology to compute $\mathbf{CF}^-$. Like with the hat theory, their minus invariants provide a recipe to compute knot invariants associated to satellite knots. We combinatorially construct the weighted $A_\infty$-modules associated to the $(p, 1)$-cable. The operations on these modules count certain classes of inductively constructed decorated planar graphs. This description of the weighted $A_\infty$-modules provides a combinatorial proof of the $A_\infty$ structure relations for the modules. We further prove a uniqueness property for the modules we construct: any weighted extensions of the unweighted $U = 0$ modules have isomorphic associated type D modules. |
| title | Bordered Heegaard Floer modules for satellite operations using planar graphs |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2506.04222 |