1 citations · 2 across the 10 of their papers we have counts for
10 papers · 1 filter
A continuum of coarse medians for all mapping class groups and right-angled groups
Giorgio Mangioni
It is shown that the mapping class group of any non-sporadic surface admits a continuum of equivariant coarse median structures, thus improving a previous theorem of the author. Th…
Geometric Inverse Semigroup Theory: a note on the Milnor-Schwarz Lemma for inverse monoids
Giorgio Mangioni, Francesco Tesolin
We generalise the Milnor-Schwarz lemma to inverse monoids acting on presheaves of geodesic metric spaces. We provide two proofs of this fact: one only uses elementary techniques, i…
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…
Bounded cohomology, quotient extensions, and hierarchical hyperbolicity
Francesco Fournier-Facio, Giorgio Mangioni, Alessandro Sisto
We call a central extension bounded if its Euler class is represented by a bounded cocycle. We prove that a bounded central extension of a hierarchically hyperbolic group (HHG) is…
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…
Random quotients of mapping class groups are quasi-isometrically rigid
Giorgio Mangioni
We prove several rigidity properties for random quotients of mapping class groups of surfaces, namely whose kernel is normally generated by the n-th steps of finitely many independ…
A Combinatorial Structure for Many Hierarchically Hyperbolic Spaces
Mark Hagen, Giorgio Mangioni, Alessandro Sisto
The combinatorial hierarchical hyperbolicity criterion is a very useful way of constructing new hierarchically hyperbolic spaces (HHSs). We show that, conversely, HHSs satisfying n…
Rigidity of mapping class groups mod powers of twists
Giorgio Mangioni, Alessandro Sisto
We study quotients of mapping class groups of punctured spheres by suitable large powers of Dehn twists, showing an analogue of Ivanov's theorem for the automorphisms of the corres…