Real bordered Floer homology
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908986956054528 |
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| author | Lipshitz, Robert Ozsváth, Peter |
| author_facet | Lipshitz, Robert Ozsváth, Peter |
| contents | Fix a 3-manifold $Y$ with boundary $F\amalg F$ and an orientation-preserving involution $τ: Y\to Y$ exchanging the boundary components, with nonempty fixed set. To an appropriate kind of Heegaard diagram for $Y$, we describe how to associate a module over the bordered Heegaard Floer algebra of $F$. These modules satisfy a gluing, or pairing, theorem, and extend the "hat" variant of Guth-Manolescu's real Heegaard Floer homology, $\widehat{HFR}(Y,τ)$. Using these modules, we give a practical algorithm to compute $\widehat{HFR}(Y,τ)$ for real 3-manifolds $(Y,τ)$ with connected fixed set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20565 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Real bordered Floer homology Lipshitz, Robert Ozsváth, Peter Geometric Topology Symplectic Geometry Fix a 3-manifold $Y$ with boundary $F\amalg F$ and an orientation-preserving involution $τ: Y\to Y$ exchanging the boundary components, with nonempty fixed set. To an appropriate kind of Heegaard diagram for $Y$, we describe how to associate a module over the bordered Heegaard Floer algebra of $F$. These modules satisfy a gluing, or pairing, theorem, and extend the "hat" variant of Guth-Manolescu's real Heegaard Floer homology, $\widehat{HFR}(Y,τ)$. Using these modules, we give a practical algorithm to compute $\widehat{HFR}(Y,τ)$ for real 3-manifolds $(Y,τ)$ with connected fixed set. |
| title | Real bordered Floer homology |
| topic | Geometric Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2604.20565 |