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This book provides a general framework for doing geometric group theory for many non-
locally-compact topological transformation groups that arise in mathematical practice …

It is a classical result that pure mapping class groups of connected, orientable surfaces of
finite type and genus at least 3 are perfect. In stark contrast, we construct nontrivial …

We present a general framework for automatic continuity results for groups of isometries of
metric spaces. In particular, we prove automatic continuity property for the groups of …

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

Let M be a circle or a compact interval, and let α= k+ τ ≥ 1 α= k+ τ≥ 1 be a real number
such that k= ⌊ α ⌋ k=⌊ α⌋. We write\, Diff\, _+^ α (M) Diff+ α (M) for the group of orientation …

We classify the connected orientable 2-manifolds whose mapping class groups have a
dense conjugacy class. We also show that the mapping class group of a connected …

In this paper we explore the extent to which the algebraic structure of a monoid $ M $
determines the topologies on $ M $ that are compatible with its multiplication. Specifically we …

We extend the proof of automatic continuity for homeomorphism groups of manifolds to non-
compact manifolds and manifolds with marked points and their mapping class groups …

We show that the (topological) full group of a minimal pseudogroup over the Cantor set
satisfies various rigidity phenomena of topological dynamical and combinatorial nature. Our …