Special cubulation of strict hyperbolization
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 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.
Cite
@article{arxiv.2206.03620,
title = {Special cubulation of strict hyperbolization},
author = {Jean-François Lafont and Lorenzo Ruffoni},
journal= {arXiv preprint arXiv:2206.03620},
year = {2024}
}
Comments
70 pages, 32 figures, comments are welcome. v2: Corollary 1.6 in v1 needed a relative version of our main theorem, so it has been moved to arXiv:2304.14946. v3: Theorem 1.2 has been improved and now works for any compact simplicial complex. Various minor edits to improve the exposition. Figure 20 is new. v4: minor edits. Final version to appear in Inventiones Mathematicae