From the 1 of 10 linked papers with an AI index.
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Bounded cohomology, quotient extensions, and hierarchical hyperbolicity
Francesco Fournier-Facio, Giorgio Mangioni, Alessandro Sisto
The authors introduce bounded central extensions (those whose Euler class is represented by a bounded cocycle) and prove that such extensions of hierarchically hyperbolic groups (H…
On automorphisms, quasimorphisms, and coarse automorphisms of acylindrically hyperbolic groups
Ashot Minasyan, Alessandro Sisto, Federico Vigolo
We investigate the action of the automorphism group of an acylindrically hyperbolic group G on its space of homogeneous quasimorphisms, and identify its kernel with the subgroup of…
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…
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…
Finite Index Rigidity of Relatively Hyperbolic Groups
Nir Lazarovich, Gon Rahamim, Alessandro Sisto
We prove that, given a torsion-free relatively hyperbolic group G with non-relatively-hyperbolic peripherals, isomorphic finite index subgroups of G have the same index. This appli…
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…