Related papers: Lamplighter groups and von Neumann's continuous re…

Recent work has shown that if an isostatic bar and joint framework possesses non-trivial symmetries, then it must satisfy some very simply stated restrictions on the number of joints and bars that are `fixed' by various symmetry operations…

Given a dynamical system $(X, \Gamma)$, the corresponding crossed product $C^*$-algebra $C(X)\rtimes_{r}\Gamma$ is called reflecting, when every intermediate $C^*$-algebra $C^*_r(\Gamma)<\mathcal{A} < C(X)\rtimes_{r}\Gamma$ is of the form…

It is first argued that radiation by a uniformly accelerated charge in flat space-time indicates the need for a unified geometric theory of gravity and electromagnetism. Such a theory, based on a metric-affine $U_4$ manifold, is constructed…

We introduce the first examples of groups $G$ with infinite center which in a natural sense are completely recognizable from their von Neumann algebras, $\mathcal{L}(G)$. Specifically, assume that $G=A\times W$, where $A$ is an infinite…

The notion of a $\Gamma $-symmetric space is a generalization of the classical notion of a symmetric space, where a general finite abelian group $\Gamma $ replaces the group $Z_2$. The case $\Gamma =\Z_k$ has also been studied, from the…

The theory of Lambda-rings, in the sense of Grothendieck's Riemann-Roch theory, is an enrichment of the theory of commutative rings. In the same way, we can enrich usual algebraic geometry over the ring Z of integers to produce…

Let G be a semisimple Lie group with associated symmetric space D, and let Gamma subset G be a cocompact arithmetic group. Let L be a lattice inside a Z Gamma-module arising from a rational finite-dimensional complex representation of G.…

Under some suitable assumptions Riemannian manifolds $(M, g, H)$ that admit a connection $\hat\nabla$ with torsion a 3-form $H$, which is both closed $d H=0$ and $\hat\nabla$-covariantly constant, are locally isometric to a product $N\times…

We prove that every finitely generated group $G$ discriminated by a locally quasi-convex torsion-free hyperbolic group $\Gamma$ is effectively coherent: that is, presentations for finitely generated subgroups can be computed from the…

This note contains a reformulation of the Hodge index theorem within the framework of Atiyah's $L^2$-index theory. More precisely, given a compact K\"ahler manifold $(M,h)$ of even complex dimension $2m$, we prove that…

Let $\Gamma$ be a countable abelian group. An (abstract) $\Gamma$-system $\mathrm{X}$ - that is, an (abstract) probability space equipped with an (abstract) probability-preserving action of $\Gamma$ - is said to be a Conze-Lesigne system if…

A conjecture of Benjamini & Schramm from 1996 states that any finitely generated group that is not a finite extension of Z has a non-trivial percolation phase. Our main results prove this conjecture for certain groups, and in particular…

An invariant random subgroup of the countable group {\Gamma} is a random subgroup of {\Gamma} whose distribution is invariant under conjugation by all elements of {\Gamma}. We prove that for a nonamenable invariant random subgroup H, the…

We study lattice embeddings for the class of countable groups $\Gamma$ defined by the property that the largest amenable uniformly recurrent subgroup $A_\Gamma$ is continuous. When $A_\Gamma$ comes from an extremely proximal action and the…

Let G be a connected complex simple Lie group with maximal compact subgroup U. Let g be the Lie algebra of G, and X = G/U be the associated Riemannian globally symmetric space of type IV. We have constructed three types of arithmetic…

We introduce a coarse analog of the classical Lusternik-Schnirelmann category which we denote by $\text{c-cat}$, defined for metric spaces in the coarse homotopy category. This provides a new tool for studying large-scale topological…

We discuss gravitational lensing in the Kehagias-Sfetsos space-time emerging in the framework of Ho\v{r}ava-Lifshitz gravity. In weak lensing we show that there are three regimes, depending on the value of $\bar {\lambda}=1/\omega d^{2}$,…

Let $\Gamma$ be a connected $G$-vertex-transitive graph, let $v$ be a vertex of $\Gamma$ and let $G_v^{\Gamma(v)}$ be the permutation group induced by the action of the vertex-stabiliser $G_v$ on the neighbourhood $\Gamma(v)$. The graph…

Let $\Gamma<\mathrm{PSL}_2(\mathbb{C})\simeq \mathrm{Isom}^+(\mathbb{H}^3)$ be a finitely generated non-Fuchsian Kleinian group whose ordinary set $\Omega=\mathbb{S}^2-\Lambda$ has at least two components. Let $\rho : \Gamma \to…

Let $S_n$ denote the symmetric group on $n$ elements, and $\Sigma\subseteq S_{n}$ a symmetric subset of permutations. Aldous' spectral gap conjecture, proved by Caputo, Liggett and Richthammer [arXiv:0906.1238], states that if $\Sigma$ is a…