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We show that a large class of i.c.c., countable, discrete groups satisfying a weak negative curvature condition are not inner amenable. By recent work of Hull and Osin, our result recovers that mapping class groups and Out(F_n) are not…

Operator Algebras · Mathematics 2019-02-20 Ionut Chifan , Thomas Sinclair , Bogdan Udrea

We study Measurable Imbeddability between groups, which is an order-like generalization of Measure Equivalence that allows the imbedded group to have an infinite measure fundamental domain. We prove if $\Lambda_1$ measurably imbeds into…

Group Theory · Mathematics 2024-03-29 Özkan Demir

We review and study some of the properties of smooth Gaussian random fields defined on a homogeneous space, under the assumption that the probability distribution is invariant under the isometry group of the space. We first give an…

Probability · Mathematics 2022-04-22 Alexandre Afgoustidis

We prove that if a countable group $\Gamma$ contains infinite commuting subgroups $H, H'\subset \Gamma$ with $H$ non-amenable and $H'$ ``weakly normal'' in $\Gamma$, then any measure preserving $\Gamma$-action on a probability space which…

Group Theory · Mathematics 2007-12-25 Sorin Popa

Let L be a Lie group and Lambda a lattice in L. Suppose G is a non-compact simple Lie group realized as a Lie subgroup of L, and the image of G on L/Lambda is dense. Let c be a diagonalizable element of G not contained in a compact…

Representation Theory · Mathematics 2007-05-23 Nimish A. Shah

We explore the structure of the p-adic automorphism group Gamma of the infinite rooted regular tree. We determine the asymptotic order of a typical element, answering an old question of Turan. We initiate the study of a general dimension…

Group Theory · Mathematics 2011-11-10 Miklos Abert , Balint Virag

This work gives an equivariantly enriched count of nodal orbits in a general pencil of plane conics that is invariant under a linear action of a finite group on $\mathbb{CP}^2$. This is both inspired by and a departure from $R(G)$-valued…

Algebraic Geometry · Mathematics 2025-05-05 Candace Bethea

We study the dynamics of countable groups on their respective spaces of quasimorphisms. For cohomologically non-trivial quasimorphisms we show that there are no invariant measures and classify stationary measures. Within the equivalence…

Dynamical Systems · Mathematics 2023-12-22 Michael Björklund , Tobias Hartnick

We classify invariant probability measures for non-elementary groups of automorphisms, on any compact K\"ahler surface X, under the assumption that the group contains a so-called "parabolic automorphism". We also prove that except in…

Dynamical Systems · Mathematics 2022-02-10 Serge Cantat , Romain Dujardin

In a previous paper we introduced a version of associativity for a partial infinitary operation. We prove here that if $\gamma$ is an infinite ordinal and some associative infinitary operation is defined for all sequences indexed by…

Logic · Mathematics 2026-05-28 Paolo Lipparini

In this letter we show that the soft behaviour of photons and graviton amplitudes, after projection, can be determined to infinite order in soft expansion via ordinary on-shell gauge invariance. In particular, as one of the particle's…

High Energy Physics - Theory · Physics 2018-08-15 Zhi-Zhong Li , Hung-Hwa Lin , Shun-Qing Zhang

Semigroup actions and their invertible extensions are discussed. First, we develop a theory of natural extensions for continuous actions of countable, embeddable semigroups. Second, we demonstrate that not every surjective such action of a…

Dynamical Systems · Mathematics 2025-07-14 Raimundo Briceño , Álvaro Bustos-Gajardo , Miguel Donoso-Echenique

In this article we study the space of left- and bi-invariant orderings on a torsion-free nilpotent group $G$. We will show that generally the set of such orderings is equipped with a faithful action of the automorphism group of $G$. We…

Geometric Topology · Mathematics 2011-12-06 Thomas Koberda

Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion…

Representation Theory · Mathematics 2010-12-06 Gestur Olafsson , Joseph A. Wolf

We present a new approach to the proof of ergodic theorems for actions of free groups based on geometric covering and asymptotic invariance arguments. Our approach can be viewed as a direct generalization of the classical geometric covering…

Dynamical Systems · Mathematics 2010-09-03 Lewis Bowen , Amos Nevo

Schreier graphs, which possess both a graph structure and a Schreier structure (an edge-labeling by the generators of a group), are objects of fundamental importance in group theory and geometry. We study the Schreier structures with which…

Dynamical Systems · Mathematics 2014-06-02 Jan Cannizzo

We investigate compact quantum group actions on unital $C^*$-algebras by analyzing invariant subsets and invariant states. In particular, we come up with the concept of compact quantum group orbits and use it to show that countable compact…

Operator Algebras · Mathematics 2015-11-17 Huichi Huang

The notion of expansivity and its generalizations (measure expansive, measure positively expansive, continuum-wise expansive, countably-expansive) are well known for deterministic systems and can be a useful property for studying…

Dynamical Systems · Mathematics 2024-10-15 Rafael A. Bilbao , Marlon Oliveira , Eduardo Santana

We show that certain orderable groups admit no isolated left orders. The groups we consider are cyclic amalgamations of a free group with a general orderable group, the HNN extensions of free groups over cyclic subgroups, and a particular…

Group Theory · Mathematics 2018-12-19 Juan Alonso , Joaquin Brum

In this paper we characterize spaces of $L^\infty$-functions on a compact Hausdorff space that are invariant under a transitive and continuous group action. This work generalizes the author's 2021 results concerning the specific case of…

Functional Analysis · Mathematics 2022-06-06 Samuel A. Hokamp
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