Computing Heegaard Floer invariants of closed contact 3-manifolds from open books
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916597413707776 |
|---|---|
| author | Kutluhan, Cagatay Matic, Gordana Van Horn-Morris, Jeremy Wand, Andy |
| author_facet | Kutluhan, Cagatay Matic, Gordana Van Horn-Morris, Jeremy Wand, Andy |
| contents | We present two SageMath programs that build on and improve upon Sucharit Sarkar's hf-hat. Given an abstract open book and a collection of pairwise disjoint properly embedded arcs on a page of the open book, the first program, hf-hat-obd, can be used to analyze the resulting Heegaard diagram, while the second, hf-hat-obd-nice computes the hat version of Heegaard Floer homology of the closed oriented 3-manifold described by the Heegaard diagram as long as the latter is nice. We also provide an auxiliary program, makenice, that can be used to produce a nice Heegaard diagram out of any abstract open book and a collection of pairwise disjoint properly embedded arcs on a page of the open book. The primary applications of hf-hat-obd-nice are to the computation of the Ozsváth--Szabó contact invariant and to the detection of finiteness of spectral order, which is a Stein fillability obstruction that is stronger than the vanishing of the Ozsváth--Szabó contact invariant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02403 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computing Heegaard Floer invariants of closed contact 3-manifolds from open books Kutluhan, Cagatay Matic, Gordana Van Horn-Morris, Jeremy Wand, Andy Geometric Topology Symplectic Geometry 57K33, 57R58 We present two SageMath programs that build on and improve upon Sucharit Sarkar's hf-hat. Given an abstract open book and a collection of pairwise disjoint properly embedded arcs on a page of the open book, the first program, hf-hat-obd, can be used to analyze the resulting Heegaard diagram, while the second, hf-hat-obd-nice computes the hat version of Heegaard Floer homology of the closed oriented 3-manifold described by the Heegaard diagram as long as the latter is nice. We also provide an auxiliary program, makenice, that can be used to produce a nice Heegaard diagram out of any abstract open book and a collection of pairwise disjoint properly embedded arcs on a page of the open book. The primary applications of hf-hat-obd-nice are to the computation of the Ozsváth--Szabó contact invariant and to the detection of finiteness of spectral order, which is a Stein fillability obstruction that is stronger than the vanishing of the Ozsváth--Szabó contact invariant. |
| title | Computing Heegaard Floer invariants of closed contact 3-manifolds from open books |
| topic | Geometric Topology Symplectic Geometry 57K33, 57R58 |
| url | https://arxiv.org/abs/2502.02403 |