Related papers: Measure equivalence rigidity of the mapping class …

We prove an operator algebraic superrigidity statement for homomorphisms of irreducible lattices, and also their commensurators, in certain higher-rank groups into unitary groups of finite factors. This extends the authors' previous work…

We define orbifold mapping class groups (with marked points) and study them using their action on certain orbifold analogs of arcs and simple closed curves. Moreover, we establish a Birman exact sequence for suitable subgroups of orbifold…

This paper characterizes the maximum mean discrepancies (MMD) that metrize the weak convergence of probability measures for a wide class of kernels. More precisely, we prove that, on a locally compact, non-compact, Hausdorff space, the MMD…

We consider special subclasses of the class of Lindel\"of Sigma-spaces obtained by imposing restrictions on the weight of the elements of compact covers that admit countable networks: A space $X$ is in the class $L\Sigma(\leq\kappa)$ if it…

Rank-one symmetric spaces carry a solvable group model which have a generalization to a larger class of Lie groups that are one-dimensional extensions of nilpotent groups. By examining some metric properties of these symmetric spaces, we…

We completely classify the orientable infinite-type surfaces $S$ such that $\operatorname{PMap}(S)$, the pure mapping class group, has automatic continuity. This classification includes surfaces with noncompact boundary. In the case of…

We identify the smooth metrics $\mc{M}(M)$ on a manifold $M^n$ with the smooth isometric embeddings $f_g: (M,g) \rightarrow (\mb{S}^{\tn}, \tg)$ into a standard sphere of large dimension $\tn=\tn(n)$, and their Palais isotopic deformations,…

We strengthen the analogy between convex co-compact Kleinian groups and convex co-compact subgroups of the mapping class group of a surface (in the sense of B. Farb and L. Mosher).

We construct, in locally compact, second countable, amenable groups, sets with large density that fail to have certain combinatorial properties. For the property of being a shift of a set of measurable recurrence we show that this is…

This paper proves the polynomial equivalence of a broad class of definitions of quantum computational complexity. We study right-invariant metrics on the unitary group -- often called `complexity geometries' following the definition of…

The hyperelliptic mapping class group has been studied in various contexts within topology and algebraic geometry. What makes this study tractable is that there is a surjective map from the hyperelliptic mapping class group to a mapping…

We classify complex projective surfaces with an automorphism of positive entropy for which the unique invariant measure of maximal entropy is absolutely continuous with respect to Lebesgue measure.

In this article we extend the notion of $L^p$-measure subgroups couplings, a quantitative asymmetric version of measure equivalence that was introduced by Delabie, Koivisto, Le Ma\^itre and Tessera for finitely generated groups, to the…

We give some new characterizations of exactness for locally compact second countable groups. In particular, we prove that a locally compact second countable group is exact if and only if it admits a topologically amenable action on a…

A locally compact group $G$ is a cocompact envelope of a group $\Gamma$ if $G$ contains a copy of $\Gamma$ as a discrete and cocompact subgroup. We study the problem that takes two finitely generated groups $\Gamma,\Lambda$ having a common…

It is proven that the orbit-equivalence class of any essentially free probability-measure-preserving action of a free group $G$ is weakly dense in the space of actions of $G$.

We prove that many completeness properties coincide in metric spaces, precompact groups and dense subgroups of products of separable metric groups. We apply these results to function spaces C_p(X,G) of G-valued continuous functions on a…

Consider a countable group Gamma acting ergodically by measure preserving transformations on a probability space (X,mu), and let R_Gamma be the corresponding orbit equivalence relation on X. The following rigidity phenomenon is shown: there…

A coarse compactification of a proper metric space $X$ is any compactification of $X$ that is dominated by its Higson compactification. In this paper we describe the maximal coarse compactification of $X$ whose corona is of dimension $0$.…

A subcomplex $X\leq \mathcal{C}$ of a simplicial complex is strongly rigid if every locally injective, simplicial map $X\to\mathcal{C}$ is the restriction of a unique automorphism of $\mathcal{C}$. Aramayona and the second author proved…