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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.02808 |
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| _version_ | 1866910814756143104 |
|---|---|
| author | Ni, Yi |
| author_facet | Ni, Yi |
| contents | Given a compact, oriented, connected surface $F$, we show that the set of connected sutured manifolds $(M,γ)$ with $R_{\pm}(γ)\cong F$ is generated by the product sutured manifold $(F,\partial F)\times[0,1]$ through surgery triads. This result has applications in Floer theories of $3$--manifolds. The special case when $F=D^2$ or $S^2$ has been a folklore theorem, which has already been used by experts before. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02808 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generation of sutured manifolds Ni, Yi Geometric Topology Given a compact, oriented, connected surface $F$, we show that the set of connected sutured manifolds $(M,γ)$ with $R_{\pm}(γ)\cong F$ is generated by the product sutured manifold $(F,\partial F)\times[0,1]$ through surgery triads. This result has applications in Floer theories of $3$--manifolds. The special case when $F=D^2$ or $S^2$ has been a folklore theorem, which has already been used by experts before. |
| title | Generation of sutured manifolds |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2502.02808 |