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Given a 2-manifold, a fundamental question to ask is which groups can be realized as the
isometry group of a Riemannian metric of constant curvature on the manifold. In this paper …

In this article, we are concerned with various aspects of arcs on surfaces. In the first part, we
deal with topological aspects of arcs and their complements. We use this understanding, in …

For a locally finite graph $\Gamma $, we consider its mapping class group $\text
{Map}(\Gamma) $ as defined by Algom-Kfir-Bestvina. For these groups, we prove a …

We answer two questions about the topology of end spaces of infinite type surfaces and the
action of the mapping class group that have appeared in the literature. First, we give …

We address the question of determining which mapping class groups of infinite-type
surfaces admit nonelementary continuous actions on hyperbolic spaces. More precisely, let …

We construct the first examples of normal subgroups of mapping class groups that are
isomorphic to non-free right-angled Artin groups. Our construction also gives normal, non …

We prove that the mapping class group of the one‐holed Cantor tree surface is acyclic. This
in turn determines the homology of the mapping class group of the once‐punctured Cantor …

We provide a complete classification of when the homeomorphism group of a stable surface,
$\Sigma $, has the automatic continuity property: Any homomorphism from Homeo …

Given an irreducible, end‐periodic homeomorphism f: S→ S f:S→S of a surface with finitely
many ends, all accumulated by genus, the mapping torus, M f M_f, is the interior of a …