Torus decomposition and foliation detected slopes
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910930031345664 |
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| author | Lyu, Qingfeng |
| author_facet | Lyu, Qingfeng |
| contents | Let $M_1$ and $M_2$ be knot manifolds and $M=M_1\cup_f M_2$ be the closed 3-manifold obtained by gluing up $M_1$ and $M_2$ via $f:\partial M_1\xrightarrow{\cong} \partial M_2$. We show that if $M$ admits a co-oriented taut foliation, then $f$ identifies some CTF-detected rational boundary slopes of $M_1$ and $M_2$, affirming a conjecture proposed by Boyer, Gordon and Hu. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03928 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Torus decomposition and foliation detected slopes Lyu, Qingfeng Geometric Topology 57K30, 57R30 Let $M_1$ and $M_2$ be knot manifolds and $M=M_1\cup_f M_2$ be the closed 3-manifold obtained by gluing up $M_1$ and $M_2$ via $f:\partial M_1\xrightarrow{\cong} \partial M_2$. We show that if $M$ admits a co-oriented taut foliation, then $f$ identifies some CTF-detected rational boundary slopes of $M_1$ and $M_2$, affirming a conjecture proposed by Boyer, Gordon and Hu. |
| title | Torus decomposition and foliation detected slopes |
| topic | Geometric Topology 57K30, 57R30 |
| url | https://arxiv.org/abs/2505.03928 |