Cubulating Drilled bundles over graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909886205394944 |
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| author | Mj, Mahan Nag, Biswajit |
| author_facet | Mj, Mahan Nag, Biswajit |
| contents | We start with a Gromov-hyperbolic surface bundle $E$ over a graph, and drill out essential simple closed curves from fibers to obtain a drilled bundle $F$. We prove that for such drilled bundles $F$, the fundamental group $π_1(F)$ is relatively hyperbolic with $(\mathbb{Z}\oplus \mathbb{Z})$ peripheral groups. Combining the relative hyperbolicity of $π_1(F)$ thus obtained with a theorem of Wise, we establish virtually special cubulability of $π_1(F)$ provided that the maximal undrilled subbundles of $F$ are cubulable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_16403 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cubulating Drilled bundles over graphs Mj, Mahan Nag, Biswajit Group Theory Geometric Topology 20F65, 20F67 (Primary), 22E40, 57M50 We start with a Gromov-hyperbolic surface bundle $E$ over a graph, and drill out essential simple closed curves from fibers to obtain a drilled bundle $F$. We prove that for such drilled bundles $F$, the fundamental group $π_1(F)$ is relatively hyperbolic with $(\mathbb{Z}\oplus \mathbb{Z})$ peripheral groups. Combining the relative hyperbolicity of $π_1(F)$ thus obtained with a theorem of Wise, we establish virtually special cubulability of $π_1(F)$ provided that the maximal undrilled subbundles of $F$ are cubulable. |
| title | Cubulating Drilled bundles over graphs |
| topic | Group Theory Geometric Topology 20F65, 20F67 (Primary), 22E40, 57M50 |
| url | https://arxiv.org/abs/2310.16403 |