5 papers
Cusped spaces for hierarchically hyperbolic groups, and applications to Dehn filling quotients
Giorgio Mangioni, Alessandro Sisto
We introduce a construction that simultaneously yields cusped spaces of relatively hyperbolic groups, and spaces quasi-isometric to Teichmueller metrics. We use this to study Dehn-…
Random quotients preserve acylindrical and hierarchical hyperbolicity
Carolyn Abbott, Daniel Berlyne, Giorgio Mangioni +2
We propose a new model for random quotients of groups using independent random walks. In this model, we show that random quotients of acylindrical hyperbolic groups asymptotically…
Short hierarchically hyperbolic groups II: quotients and the Hopf property for Artin groups
Giorgio Mangioni, Alessandro Sisto
We prove that most Artin groups of large and hyperbolic type are Hopfian, meaning that every self-epimorphism is an isomorphism. The class covered by our result is generic, in the…
Short hierarchically hyperbolic groups I: uncountably many coarse median structures
Giorgio Mangioni
We prove that the mapping class group of a sphere with five punctures admits uncountably many coarsely equivariant coarse median structures. The same is shown for right-angled Arti…
A combination theorem for hierarchically quasiconvex subgroups, and application to geometric subgroups of mapping class groups
Giorgio Mangioni
We provide sufficient conditions for two subgroups of a hierarchically hyperbolic group to generate an amalgamated free product over their intersection. The result applies in parti…