Related papers: $L^p$ measure equivalence of nilpotent groups

By studying the group of self homotopy equivalences of the localization (at a prime $p$ and/or zero) of some aspherical complexes, we show that, contrary to the case when the considered space is a nilpotent complex, $\mathcal{E}_{\#}^m…

We get asymptotics for the volume of large balls in an arbitrary locally compact group G with polynomial growth. This is done via a study of the geometry of G and a generalization of P. Pansu's thesis. In particular, we show that any such G…

We derive sharp estimates comparing asymptotic Riemannian or sub-Riemannian metrics in 2-step nilpotent Lie groups. For each metric, we construct a Carnot metric whose square remains at bounded distance from the square of the original…

In this paper, we examine Lie group actions on moduli spaces (sets themselves built as quotients by group actions) and their fixed points. We show that when the Lie group is compact and connected, we obtain a linear constraint. This…

A topological group is (openly) almost-elliptic if it contains a(n open) dense subset of elements generating relatively-compact cyclic subgroups. We classify the (openly) almost-elliptic connected locally compact groups as precisely those…

In \cite{Kramer11} Kramer proves for a large class of semisimple Lie groups that they admit just one locally compact $\sigma$-compact Hausdorff topology compatible with the group operations. We present two different methods of generalising…

Based on the work of Adams and Stuck as well as on the work of Zeghib, we classify the Lie groups which can act isometrically and locally effectively on Lorentzian manifolds of finite volume. In the case that the corresponding Lie algebra…

We study the L^p-distortion of finite quotients of amenable groups. In particular, for every number p larger or equal than 2, we prove that the l^p-distortion of the finite lamplighter group grows like (\log n)^{1/p}. We also give the…

This article is concerned with measure equivalence and uniform measure equivalence of locally compact, second countable groups. We show that two unimodular, locally compact, second countable groups are measure equivalent if and only if they…

This is a sequel to \cite{osy} and \cite{sxy}. Associated with $G:=\GL_n$ and its rational representation $(\rho, M)$ over an algebraically closed filed $\bk$, we define an enhanced algebraic group $\uG:=G\ltimes_\rho M$ which is a product…

Answering a question by Chatterji--Dru\c{t}u--Haglund, we prove that, for every locally compact group $G$, there exists a critical constant $p_G \in [0,\infty]$ such that $G$ admits a continuous affine isometric action on an $L_p$ space…

We prove that the Heisenberg groups can be distinguished from the other connected and simply connected Lie groups via their group $C^*$-algebras. The main step of the proof is a characterization of the nilpotent Lie groups among the…

When a discrete group admits a convex-cocompact action on a non-compact rank-one symmetric space, there is a natural lower bound for the Hausdorff dimension of the limit set, given by the Ahlfors regular conformal dimension of the boundary…

We single out a large class of groups ${\mathscr{M}}$ for which the following unique prime factorization result holds: if $\Gamma_1,\dots,\Gamma_n\in {\mathscr{M}}$ and $\Gamma_1\times\dots\times\Gamma_n$ is measure equivalent to a product…

In this paper we present new examples of simple $p$-local compact groups for all odd primes. We also develop the necessary tools to show saturation, simpleness and the non-realizability as $p$-compact groups or compact Lie groups, which can…

This paper proves that the two homotopy theories for orbispaces given by Gepner and Henriques and by Schwede, respectively, agree by providing a zig-zag of Dwyer-Kan equivalences between the respective topologically enriched index…

A long standing open problem in the theory of hyperfinite equivalence relations asks if the orbit equivalence relation generated by a Borel action of a countable amenable group is hyperfinite. In this paper we show that this question has a…

In the paper, we introduce the concept of weight with reasonable growth on a locally compact group $G$. We verify that these weights form a natural class to work with, by examining the most common examples. We proceed with the discussion of…

We study $L^p$-theory of second-order elliptic divergence type operators with complex measurable coefficients. The major aspect is that we allow complex coefficients in the main part of the operator, too. We investigate generation of…

We develop an approach to the character theory of certain classes of finite and profinite groups based on the construction of a Lie algebra associated to such a group, but without making use of the notion of a polarization which is central…