Relative cubulation of relative strict hyperbolization
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| author | Groves, Daniel Lafont, Jean-François Manning, Jason Fox Ruffoni, Lorenzo |
| author_facet | Groves, Daniel Lafont, Jean-François Manning, Jason Fox Ruffoni, Lorenzo |
| contents | We prove that many relatively hyperbolic groups obtained by relative strict hyperbolization admit a cocompact action on a CAT(0) cubical complex. Under suitable assumptions on the peripheral subgroups, these groups are residually finite and even virtually special. We include some applications to the theory of manifolds, such as the construction of new non-positively curved Riemannian manifolds with residually finite fundamental group, and the existence of non-triangulable aspherical manifolds with virtually special fundamental group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_14946 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Relative cubulation of relative strict hyperbolization Groves, Daniel Lafont, Jean-François Manning, Jason Fox Ruffoni, Lorenzo Group Theory Differential Geometry Geometric Topology 20F67, 53C23, 20E26, 57Q15 We prove that many relatively hyperbolic groups obtained by relative strict hyperbolization admit a cocompact action on a CAT(0) cubical complex. Under suitable assumptions on the peripheral subgroups, these groups are residually finite and even virtually special. We include some applications to the theory of manifolds, such as the construction of new non-positively curved Riemannian manifolds with residually finite fundamental group, and the existence of non-triangulable aspherical manifolds with virtually special fundamental group. |
| title | Relative cubulation of relative strict hyperbolization |
| topic | Group Theory Differential Geometry Geometric Topology 20F67, 53C23, 20E26, 57Q15 |
| url | https://arxiv.org/abs/2304.14946 |