Related papers: Locally normal subgroups of simple locally compact…

We provide a mathematically rigorous definition of local approximation and demonstrate its applicability to some interesting classes of structures. In particular, we prove that any compact simple Lie group is locally approximated by finite…

We study properties and the structure of Cartan subgroups in a connected Lie group. We obtain a characterisation of Cartan subgroups which generalises W\"ustner's structure theorem for the same. We show that Cartan subgroups are same as…

We describe a class (called regular) of invariant generalized complex structures on a real semisimple Lie group G. The problem reduces to the description of admissible pairs (\gk, \omega), where \gk is an appropriate regular subalgebra of…

We prove that groups definable in o-minimal structures have Cartan subgroups, and only finitely many conjugacy classes of such subgroups. We also delineate with precision how these subgroups cover the ambient group, in general very largely…

Let $\Gamma$ be a finitely generated cocompact lattice of a totally disconnected locally compact group $G$, and $C$ a dense subgroup of $G$ that contains and commensurates $\Gamma$. We study the problem of describing all finitely generated…

We prove an equivariant version of the local splitting theorem for tame Poisson structures and Poisson actions of compact Lie groups. As a consequence, we obtain an equivariant linearization result for Poisson structures whose transverse…

We introduce a class of countable groups by some abstract group-theoretic conditions. It includes linear groups with finite amenable radical and finitely generated residually finite groups with some non-vanishing $\ell^2$-Betti numbers that…

The aim of this note is to give a geometric proof for classical local rigidity of lattices in semisimple Lie groups. We are reproving well known results in a more geometric (and hopefully clearer) way.

We study left invariant locally conformally product structures on simply connected Lie groups and give their complete description in the solvable unimodular case. Based on previous classification results, we then obtain the complete list of…

We study expressive power of continuous logic in classes of (locally compact) groups. We also describe locally compact groups which are separably categorical structures.

We define Cartan subgroups in connected locally compact groups, which extends the classical notion of Cartan subgroups in Lie groups. We prove their existence and justify our choice of the definition which differs from the one given by…

We show that the holonomy group of a connected Riemannian locally symmetric space (not necessarily complete) without local flat factor is compact and has finite index in its normalizer in the orthogonal group.

A discrete subgroup $\Gamma$ of a locally compact group $H$ is called a uniform lattice if the quotient $H/\Gamma$ is compact. Such an $H$ is called an envelope of $\Gamma$. In this paper we study the problem of classifying envelopes of…

In this article we introduce and study uniform and non-uniform approximate lattices in locally compact second countable (lcsc) groups. These are approximate subgroups (in the sense of Tao) which simultaneously generalize lattices in lcsc…

We investigate the complexity of the lattice of local clones over a countably infinite base set. In particular, we prove that this lattice contains all algebraic lattices with at most countably many compact elements as complete sublattices,…

We show that if a nontrivial group admits a locally invariant ordering, then it admits uncountably many locally invariant orderings. For the case of a left-orderable group, we provide an explicit construction of uncountable families of…

We give a complete characterization of the locally compact groups that are non-elementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting…

We investigate properties of closed approximate subgroups of locally compact groups, with a particular interest for approximate lattices i.e. those approximate subgroups that are discrete and have finite co-volume. We prove an approximate…

The structure of the coincidence symmetry group of an arbitrary $n$-dimensional lattice in the $n$-dimensional Euclidean space is considered by describing a set of generators. Particular attention is given to the coincidence isometry…

Every locally compact local group is locally isomorphic to a topological group.