Alessandro Sisto

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20242026

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math.GR2025

Power quotients of surface groups and mapping class groups

Rémi Coulon, Alessandro Sisto, Henry Wilton

Let $Γ$ be the fundamental group of a closed, orientable, hyperbolic surface $S$ . The $n$ -power quotient, $Γ (n)$ , is the quotient of $Γ$ by the $n$ th powers of simple closed curves…

math.GR2025

Non-solutions to mixed equations in acylindrically hyperbolic groups coming from random walks

Henry Bradford, Alessandro Sisto

A mixed equation in a group $G$ is given by a non-trivial element $w (x)$ of the free product $G * Z$ , and a solution is some $g \in G$ such that $w (g)$ is the identity.…

math.GR2024

Cohomological characterisation of hyperbolicity

Francesco Milizia, Nansen Petrosyan, Alessandro Sisto +1

For any geodesic metric space $X$ , we give a complete cohomological characterisation of the hyperbolicity of $X$ in terms of vanishing of its second $ℓ^{\infty}$ -cohomology. We…