Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.15923 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915747426467840 |
|---|---|
| author | Honda, Ko Tian, Yin Yuan, Tianyu |
| author_facet | Honda, Ko Tian, Yin Yuan, Tianyu |
| contents | Given a closed surface $C$ and a real exact Lagrangian $Σ\subset T^*C$ associated to a spectral curve, we construct a homomorphism $\operatorname{BSk}_κ(C)\to\operatorname{Mat}(N^κ,\operatorname{BSk}_κ(Σ))$ from the braid skein algebra of $C$ to the matrix-valued braid skein algebra of $Σ$ using Floer theory and in particular higher-dimensional Heegaard Floer homology (HDHF). We sketch a proof that this map coincides with a hybrid Floer-Morse approach which counts HDHF-type holomorphic curves coupled with certain Morse gradient graphs -- called fold\-ed Morse trees -- using a variant of the adiabatic limit theorems of Fukaya-Oh and Ekholm, which compares holomorphic curves and Morse flow trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15923 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Higher-dimensional Heegaard Floer homology and spectral networks Honda, Ko Tian, Yin Yuan, Tianyu Symplectic Geometry 53D40, 57K20 Given a closed surface $C$ and a real exact Lagrangian $Σ\subset T^*C$ associated to a spectral curve, we construct a homomorphism $\operatorname{BSk}_κ(C)\to\operatorname{Mat}(N^κ,\operatorname{BSk}_κ(Σ))$ from the braid skein algebra of $C$ to the matrix-valued braid skein algebra of $Σ$ using Floer theory and in particular higher-dimensional Heegaard Floer homology (HDHF). We sketch a proof that this map coincides with a hybrid Floer-Morse approach which counts HDHF-type holomorphic curves coupled with certain Morse gradient graphs -- called fold\-ed Morse trees -- using a variant of the adiabatic limit theorems of Fukaya-Oh and Ekholm, which compares holomorphic curves and Morse flow trees. |
| title | Higher-dimensional Heegaard Floer homology and spectral networks |
| topic | Symplectic Geometry 53D40, 57K20 |
| url | https://arxiv.org/abs/2601.15923 |