Related papers: A group with Property (T) acting on the circle

Let $G$ be a group acting properly and essentially on an irreducible, non-Euclidean finite dimensional CAT(0) cube complex $X$ without fixed points at infinity. We show that for any finite collection of simultaneously inessential subgroups…

We prove that under certain topological conditions on the set of universal elements of a continuous map $T$ acting on a topological space $X$, that the direct sum $T\oplus M_g$ is universal, where $M_g$ is multiplication by a generating…

In this article, we construct partial periodic quotients of groups which have a non-elementary acylindrical action on a hyperbolic space. In particular, we provide infinite quotients of mapping class groups where a fixed power of every…

Let $Q$ be a closed manifold admitting a locally-free action of a compact Lie group $G$. In this paper we study the properties of geodesic flows on $Q$ given by Riemannian metrics which are invariant by such an action. In particular, we…

Let $\Sigma$ be a closed surface other than the sphere, the torus, the projective plane or the Klein bottle. We construct a continuum of p.m.p. ergodic minimal profinite actions for the fundamental group of $\Sigma$, that are topologically…

We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups $G$ such that every element of $G$ is contained in a compact open normal subgroup of $G$. For…

In this paper, we study the geometric property (T) for discretized warped cones of an action on a compact Lie group $M$ by its finitely generated subgroup. We show that if a subgroup $G$ is dense in $M$, then the associated discretized…

We study the topological dynamics of the action of an acylindrically hyperbolic group on the space of its infinite index convex cocompact subgroups by conjugation. We show that, for any suitable probability measure $\mu$, random walks with…

A theorem of Cantat and Urech says that an analog of the classical Tits alternative holds for the group of birational automorphisms of a compact complex Kaehler surface. We established in our previous paper the following Tits-type…

Let $H$ be a subnormal co-compact closed subgroup of a Hausdorff topological group $T$ and $X$ a compact Hausdorff space. We prove the inheritance theorem: A point of $X$ is almost periodic (a.p.) for $T\curvearrowright X$ iff it is a.p.…

A topological group is locally pseudocompact if it contains a non-empty open set with pseudocompact closure. In this note, we prove that if G is a group with the property that every closed subgroup of G is locally pseudocompact, then G_0 is…

We show that all groups of a distinguished class of \guillemotleft large\guillemotright\ topological groups, that of Roelcke precompact Polish groups, have Kazhdan's Property (T). This answers a question of Tsankov and generalizes previous…

In these lectures we consider how algebraic properties of discrete subgroups of Lie groups restrict the possible actions of those groups on surfaces. The results show a strong parallel between the possible actions of such a group on the…

The main objects of study in this article are pairs $(G, \mathcal{H})$ where $G$ is a topological group with a compact open subgroup, and $\mathcal{H}$ is a finite collection of open subgroups. We develop geometric techniques to study the…

We prove that any Lie subgroup $G$ (with finitely many connected components) of an infinite-dimensional topological group $\mathcal G$ which is an amalgamated product of two closed subgroups, can be conjugated to one factor. We apply this…

Semigroups generated by topological operations such as closure, interior or boundary are considered. It is noted that some of these semigroups are in general finite and noncommutative. The problem is formulated whether they are always…

We construct several series of explicit presentations of infinite hyperbolic groups enjoying Kazhdan's property (T). Some of them are significantly shorter than the previously known shortest examples. Moreover, we show that some of those…

A topological gyrogroup is a gyrogroup endowed with a compatible topology such that the multiplication is jointly continuous and the inverse is continuous. In this paper, we study the quotient gyrogroups in topological gyrogroups with…

Let $K$ be a nontrivial knot in $S^3$. We say that an element of the knot group $G(K)$ is \textit{persistent} if it remains nontrivial under all nontrivial Dehn fillings. Such elements exist for every nontrivial knot. Indeed, Property P is…

We show that the topological full group of a Hausdorff ample groupoid with compact unit space coincides with the group of homotopy classes of invertible isometries in pseudofunction algebras associated with the groupoid. Moreover, if the…