An Excision Theorem in Heegaard Floer Theory
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910671055093760 |
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| author | Bagherifard, Neda |
| author_facet | Bagherifard, Neda |
| contents | Let $Y_1$ be a closed, oriented 3-manifold and $Σ$ denote a non-separating closed, orientable surface in $Y_1$ which consists of two connected components of the same genus. By cutting $Y_1$ along $Σ$ and re-gluing it using an orientation-preserving diffeomorphism of $Σ$ we obtain another closed, oriented 3-manifold $Y_2$. When the excision surface $Σ$ is of genus one, we show that twisted Heegaard Floer homology groups of $Y_1$ and $Y_2$ (twisted with coefficients in the universal Novikov ring) are isomorphic. We use this excision theorem to demonstrate that certain manifolds are not related by the excision construction on a genus one surface. Additionally, we apply the excision formula to compute twisted Heegaard Floer homology groups of 0-surgery on certain two-component links, including some families of 2-bridge links. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20307 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Excision Theorem in Heegaard Floer Theory Bagherifard, Neda Geometric Topology 57R58, 57K31, 57K18 Let $Y_1$ be a closed, oriented 3-manifold and $Σ$ denote a non-separating closed, orientable surface in $Y_1$ which consists of two connected components of the same genus. By cutting $Y_1$ along $Σ$ and re-gluing it using an orientation-preserving diffeomorphism of $Σ$ we obtain another closed, oriented 3-manifold $Y_2$. When the excision surface $Σ$ is of genus one, we show that twisted Heegaard Floer homology groups of $Y_1$ and $Y_2$ (twisted with coefficients in the universal Novikov ring) are isomorphic. We use this excision theorem to demonstrate that certain manifolds are not related by the excision construction on a genus one surface. Additionally, we apply the excision formula to compute twisted Heegaard Floer homology groups of 0-surgery on certain two-component links, including some families of 2-bridge links. |
| title | An Excision Theorem in Heegaard Floer Theory |
| topic | Geometric Topology 57R58, 57K31, 57K18 |
| url | https://arxiv.org/abs/2410.20307 |