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arXiv · 2304.14946

Relative cubulation of relative strict hyperbolization

Daniel Groves·Jean-François Lafont·Jason Fox Manning·Lorenzo Ruffoni
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Abstract

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.

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Daniel Groves, Jean-François Lafont, Jason Fox Manning, Lorenzo Ruffoni. 2025-04-02. Relative cubulation of relative strict hyperbolization. https://doi.org/10.1112/jlms.70093

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