Related papers: Dynamical properties of profinite actions

We consider two operations on an edge of an embedded graph (or equivalently a ribbon graph): giving a half-twist to the edge and taking the partial dual with respect to the edge. These two operations give rise to an action of S_3^{|E(G)|},…

Let $A$ be a commutative ring, and assume every non-trivial ideal of $A$ has finite-index. We show that if ${\rm{SL}}_n(A)$ has bounded elementary generation then every conjugation-invariant norm on it is either discrete or precompact. If…

We establish $\mathcal{Z}$-stability for crossed products of outer actions of amenable groups on $\mathcal{Z}$-stable $C^*$-algebras under a mild technical assumption which we call McDuff property with respect to invariant traces. We obtain…

We survey recent results on multiple transitivity of automorphism groups of affine algebraic varieties. We consider the property of infinite transitivity of the special automorphism group, which is equivalent to flexibility of the…

We prove that Connes' Embedding Conjecture holds for the von Neumann algebras of sofic groups, that is sofic groups are hyperlinear. Hence we provide some new examples of hyperlinearity. We also show that the Determinant Conjecture holds…

A systolic complex/bridged graph is fit when its (metric) intervals are "not too large". We prove that uniformly locally finite fit systolic complexes have Yu's Property A. In particular, groups acting properly on such complexes have…

We prove that the class of residually C groups is closed under taking graph products, provided that C is closed under taking subgroups, finite direct products and that free-by-C groups are residually C. As a consequence, we show that local…

We study a class of finite groups $G$ which behave similarly to elementary abelian $p$-groups with $p$ prime, that is, there exists a subgroup $N$ such that all elements of $G\setminus N$ are conjugate or inverse-conjugate under $\Aut(G)$.…

Interactions growing slower than a certain exponential of the square of a scalar field, are well behaved when evolved under the functional renormalization group linearised around the Gaussian fixed point. They satisfy properties usually…

We establish the existence of a duality transformation for generic models of interacting fermions with two-body interactions. The eigenstates at weak and strong interaction U possess similar statistical properties when expressed in the U=0…

We show that any finitely generated non-elementary Kleinian group has a co-final family of finite index normal subgroups with respect to which it has Property $\tau$. As a consequence, any closed hyperbolic 3-manifold has a co-final family…

We extend the theory of equivariant orthogonal spectra from finite groups to profinite groups, and more generally from compact Lie groups to compact Hausdorff groups. The G-homotopy theory is "pieced together" from the G/U-homotopy theories…

In 1993, Lubotzky and Weiss conjectured that if a compact group admits two finitely generated dense subgroups, one of which is amenable and the other has Kazhdan's property (T), then it would be finite. This conjecture was resolved in the…

A group $G$ is said to have property (PH') if there exist finitely many hyperbolic spaces $X_1,\cdots,X_n$ on which $G$ acts coboundedly such that the diagonal action of $G$ on the product $\prod_{i=1}^nX_i$ equipped with $\ell^1$-metric is…

We prove that, given a torsion-free relatively hyperbolic group G with non-relatively-hyperbolic peripherals, isomorphic finite index subgroups of G have the same index. This applies for instance to fundamental groups of finite-volume…

We study some dynamical properties of the canonical Aut(F_n)-action on the space R_n(G) of redundant representations of the free group F_n in G, where G is the group of rational points of a simple algebraic group over a local field. We show…

We study a class of edge-coloured graphs, including the chamber systems of buildings and other geometries such as affine planes, from which we build coherent configurations (also known as non-commutative association schemes). The condition…

In this article we will see some properties that guarantee that a product of an ergodic non-singular action and a probability preserving ergodic action is also an ergodic action. We will start by proving 'The multiplier theorem' for locally…

Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these groups may overlap. Group memberships are generated through the bipartite configuration model.…

We show that an infinite residually finite boundedly generated group has an infinite chain of finite index subgroups with ranks uniformly bounded, and give (sublinear) upper bounds on the ranks of arbitrary finite index subgroups of…