Related papers: Large scale properties for bounded automata groups
A topological group $G$ is said to have a local $\omega^\omega$-base if the neighbourhood system at identity admits a monotone cofinal map from the directed set $\omega^\omega$. In particular, every metrizable group is such, but the class…
We study finite semigroups of $n \times n$ matrices with rational entries. Such semigroups provide a rich generalization of transition monoids of unambiguous (and, in particular, deterministic) finite automata. In this paper we determine…
Possible forms of obstructed atomic limits in quasi-one-dimensional systems are studied using line group symmetry. This is accomplished by revisiting the standard theory with an emphasis on its group-theoretical background, synthesizing the…
We show that compact complex manifolds of algebraic dimension zero bearing a holomorphic Cartan geometry of algebraic type have infinite fundamental group. This generalizes the main Theorem in [DM] where the same result was proved for the…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
We study mapping class groups of infinite type surfaces with isolated punctures and their actions on the loop graphs introduced by Bavard-Walker. We classify all of the mapping classes in these actions which are loxodromic with a WWPD…
Automata over infinite words, also known as omega-automata, play a key role in the verification and synthesis of reactive systems. The spectrum of omega-automata is defined by two characteristics: the acceptance condition (e.g. B\"uchi or…
We consider classes of diffeomorphisms of Euclidean space with partial asymptotic expansions at infinity; the remainder term lies in a weighted Sobolev space whose properties at infinity fit with the desired application. We show that two…
Let S be any orientable surface of infinite genus with a finite number of boundary components. In this work we consider the curve complex C(S), the nonseparating curve complex N(S) and the Schmutz graph G(S) of S. When all the topological…
In this paper we look at the automorphisms of the multiplicative group of finite nearfields. We find partial results for the actual automorphism groups. We find counting techniques for the size of all finite nearfields. We then show that…
: Algebraic properties of orbifold models on arbitrary Riemann surfaces are investigated. The action of mapping class group transformations and of standard geometric operations is given explicitly. An infinite dimensional extension of the…
The present article constitutes the third part of our study of the large scale geometry of metrisable groups, the first two part appearing in the companion paper "Large scale geometry of metrisable groups". In this third part, we present a…
In this survey, we describe recent progress on asymptotic properties of various automorphic orbits in free groups. In particular, we address the problem of counting potentially positive elements of a given length. We also discuss complexity…
Take a bounded symmetric domain $D$ and an arithmetic subgroup $\Gamma$ of ${\rm Aut}(D)$. Take the quotient $D/\Gamma$, compactify and resolve the singularities. We study the fundamental group of the compact complex manifolds that result…
We will review the main results concerning the automorphism groups of saturated structures which were obtained during the two last decades. The main themes are: the small index property in the countable and uncountable cases; the…
We investigate some properties of topological groups related to disconnectedness or Archimedeanness. We prove or disprove the preservation of those under operations as subgroups, quotients, products, etc. Characterizations of…
We analyse omega-categorical precompact expansions of particular omega-categorical structures from the viewpoint of amenability of their automorphism groups. The main result of the paper corrects and simplifies Section 3.2 of the first…
A complete geometric classification of symmetries of autonomous Hamiltonian mechanical systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results…
Stable subgroups and the Morse boundary are two systematic approaches to collect and study the hyperbolic aspects of finitely generated groups. In this paper we unify and generalize these strategies by viewing any geodesic metric space as a…
We completely classify the locally finite, infinite graphs with pure mapping class groups admitting a coarsely bounded generating set. We also study algebraic properties of the pure mapping class group: We establish a semidirect product…