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 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.
Cite
@article{arxiv.2304.14946,
title = {Relative cubulation of relative strict hyperbolization},
author = {Daniel Groves and Jean-François Lafont and Jason Fox Manning and Lorenzo Ruffoni},
journal= {arXiv preprint arXiv:2304.14946},
year = {2025}
}
Comments
29 pages, 5 figures. Main document by J.-F. Lafont and L. Ruffoni, appendix by D. Groves and J. F. Manning. Comments welcome! v2: revised final version to appear on the Journal of the London Mathematical Society