Rational surgery exact triangles in Heegaard Floer homology
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911366246301696 |
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| author | Nahm, Gheehyun |
| author_facet | Nahm, Gheehyun |
| contents | We construct a new family of surgery exact triangles in Heegaard Floer theory over the field with two elements. This family generalizes both Ozsváth and Szabó's $n$- and $1/n$-surgery exact triangles for positive integers $n$ and the author's recent 2-surgery exact triangle to all positive rational slopes.
The construction reduces to a combinatorial problem that involves triangle and quadrilateral counting maps in a genus 1 Heegaard diagram. The main contribution of this paper is solving this combinatorial problem, which is particularly tricky for slopes $r\neq n,1/n$; one key idea is to use an involution that is closely related to the ${\rm Spin}^{c}$ conjugation symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06654 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rational surgery exact triangles in Heegaard Floer homology Nahm, Gheehyun Geometric Topology We construct a new family of surgery exact triangles in Heegaard Floer theory over the field with two elements. This family generalizes both Ozsváth and Szabó's $n$- and $1/n$-surgery exact triangles for positive integers $n$ and the author's recent 2-surgery exact triangle to all positive rational slopes. The construction reduces to a combinatorial problem that involves triangle and quadrilateral counting maps in a genus 1 Heegaard diagram. The main contribution of this paper is solving this combinatorial problem, which is particularly tricky for slopes $r\neq n,1/n$; one key idea is to use an involution that is closely related to the ${\rm Spin}^{c}$ conjugation symmetry. |
| title | Rational surgery exact triangles in Heegaard Floer homology |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2601.06654 |