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Abstract 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$$\operatorname {CAT}(0)$$ 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.
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Relative cubulation of relative strict hyperbolization
Abstract We prove that many relatively hyperbolic groups obtained by relative strict hyperbolization admit a cocompact action on a 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.
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- Award ID(s):
- 2407438
- PAR ID:
- 10601142
- Publisher / Repository:
- Oxford University Press (OUP)
- Date Published:
- Journal Name:
- Journal of the London Mathematical Society
- Volume:
- 111
- Issue:
- 4
- ISSN:
- 0024-6107
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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