Related papers: Locally compact groups and continuous logic

We examine subgroups of locally compact groups that are continuous homomorphic images of connected Lie groups and we give a criterion for being such an image. We also provide a new characterisation of Lie groups and a characterisation of…

We define a class of spaces on which one may generalise the notion of compactness following motivating examples from higher-dimensional number theory. We establish analogues of several well-known topological results (such as Tychonoff's…

We construct classifying spaces for discrete and compact Lie groups, with the property that they are topological groups and complete metric spaces in a natural way. We sketch a program in view of extending these constructions.

The study of localizations of groups has concentrated on group theoretic properties which are preserved by localization. In this paper we look at finitely generated soluble groups and determine when the local groups associated with them are…

We begin the study of categorical logic for continuous model theory. In particular, we 1. introduce the notions of metric logical categories and functors as categorical equivalents of a metric theory and interpretations, 2. prove a…

We develop the theory of locally small spaces in a new simple language and apply this simplification to re-build the theory of locally definable spaces over structures with topologies.

Pro-$p$ groups of finite powerful class are studied. We prove that these are $p$-adic analytic, and further describe their structure when their powerful class is small. It is also shown that there are only finitely many finite $p$-groups of…

The purpose of this survey is to describe how locally compact groups can be studied as geometric objects. We will emphasize the main ideas and skip or just sketch most proofs, often referring the reader to our much more detailed book…

We give a classification of unitary representations of certain Polish, not necessarily locally compact, groups: the groups of all measurable functions with values in the circle and the groups of all continuous functions on compact, second…

We introduce the notion of commability between locally compact groups, namely the equivalence relation generated by cocompact inclusions and quotients by compact normal subgroups. We give a classification of focal hyperbolic locally compact…

We describe simply connected compact exceptional simple Lie groups in very elementary way. We first construct all simply connected compact exceptional Lie groups G concretely. Next, we find all involutive automorphisms of G, and determine…

We consider the logic space of countable (enumerated) groups and show that closed subspaces corresponding to some standard classes of groups have (do not have) generic groups. We also discuss the cases of semigroups and associative rings.

We introduce moment maps for continuous unitary representations of general topological groups. For solvable separable locally compact groups, we prove that the closure of the image of the moment map of any representation is convex.

A locally compact contraction group is a pair (G,f) where G is a locally compact group and f an automorphism of G which is contractive in the sense that the forward orbit under f of each g in G converges to the neutral element e, as n tends…

We develop the theory of locally analytic representations of compact $p$-adic Lie groups from the perspective of the theory of condensed mathematics of Clausen and Scholze. As an application, we generalise Lazard's isomorphisms between…

We investigate a family of rule-based logics. The focus is on very expressive languages. We provide a range of characterization results for the expressive powers of the logics and relate them with corresponding game systems.

The unitary representation theory of locally compact contraction groups and their semi-direct products with $\mathbb{Z}$ is studied. We put forward the problem of completely characterising such groups which are type I or CCR and this…

We analyze definably compact groups in o-minimal expansions of ordered groups as a combination of semi-linear groups and groups definable in o-minimal expansions of real closed fields. The analysis involves structure theorems about their…

Recently we have shown a structure theorem for locally compact groups of polynomial growth. We give now some applications on various growth functions and relations to FC-G - series. In addition, we show some results on related classes of…

We show that the categories of compact Lie groups and complex reductive groups (not necessarily connected) are homotopy equivalent topological categories. In other words, the corresponding categories enriched in the homotopy category of…