Special cubulation of strict hyperbolization
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866929556867252224 |
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| author | Lafont, Jean-François Ruffoni, Lorenzo |
| author_facet | Lafont, Jean-François Ruffoni, Lorenzo |
| contents | We prove that the Gromov hyperbolic groups obtained by the strict hyperbolization procedure of Charney and Davis are virtually compact special, hence linear and residually finite. Our strategy consists in constructing an action of a hyperbolized group on a certain dual CAT(0) cubical complex. As a result, all the common applications of strict hyperbolization are shown to provide manifolds with virtually compact special fundamental group. In particular, we obtain examples of closed negatively curved Riemannian manifolds whose fundamental groups are linear and virtually algebraically fiber. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2206_03620 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Special cubulation of strict hyperbolization Lafont, Jean-François Ruffoni, Lorenzo Group Theory Differential Geometry Geometric Topology 20F67, 53C23, 20E26, 57Q05 We prove that the Gromov hyperbolic groups obtained by the strict hyperbolization procedure of Charney and Davis are virtually compact special, hence linear and residually finite. Our strategy consists in constructing an action of a hyperbolized group on a certain dual CAT(0) cubical complex. As a result, all the common applications of strict hyperbolization are shown to provide manifolds with virtually compact special fundamental group. In particular, we obtain examples of closed negatively curved Riemannian manifolds whose fundamental groups are linear and virtually algebraically fiber. |
| title | Special cubulation of strict hyperbolization |
| topic | Group Theory Differential Geometry Geometric Topology 20F67, 53C23, 20E26, 57Q05 |
| url | https://arxiv.org/abs/2206.03620 |