Related papers: A note on properly discontinuous actions
Let a group $G$ act properly discontinuously and cocompactly on a locally compact space $X$. A Hausdorff compact space $Z$ that contains $X$ as an open subspace has the perspectivity property if the action $G\curvearrowright X$ extends to…
We define directional recurrence for infinite measure preserving Z^d actions both intrinsically and via the unit suspension flow and prove that the two definitions are equivalent. We study the structure of the set of recurrent directions…
We determine a fundamental domain for the diagonal action of a finite Coxeter group $W$ on $V^{\oplus n}$, where $V$ is the reflection representation. This is used to give a stratification of $V^{\oplus n}$, which is respected by the group…
When a finite group freely acts on a topological space, we can define its index and coindex. They roughly measure the size of the given action. We explore the interaction between this index theory and topological dynamics. Given a…
We give sufficient conditions for sensitivity of continuous group actions on uniform spaces.
Traces and their extension called combined traces (comtraces) are two formal models used in the analysis and verification of concurrent systems. Both models are based on concepts originating in the theory of formal languages, and they are…
We introduce a general notion of covering property, of which many classical definitions are particular instances. Notions of closure under various sorts of convergence, or, more generally, under taking kinds of accumulation points, are…
A monoid $S$ is right coherent if every finitely generated subact of every finitely presented right $S$-act is finitely presented. This is a finiteness condition, and we investigate whether or not it is preserved under some standard…
Groups with a topology that is in consistent one way or another with the algebraic structure are considered. Classical groups with a topology are topological, paratopological, semitopological, and quasitopological groups. We also study…
The survey presents the main developments obtained over the last decade regarding pointwise ergodic theorems for measure preserving actions of locally compact groups. The survey includes an exposition of the solutions to a number of long…
We study actions of connected algebraic groups on normal algebraic varieties, and show how to reduce them to actions of affine subgroups.
An isometric action of a Lie group on a Riemannian manifold is of cohomogeneity one if the corresponding orbit space is one-dimensional. In this article we develop a conceptual approach to the classification of cohomogeneity one actions on…
We establish a Lichnerowicz type vanishing theorem for non-compact spin manifolds admiting proper cocompact actions, when the action group is unimodular.
We introduce the notions of definable amenability and extreme definable amenability for groups in continuous structures and conduct an extensive analysis of them, drawing parallels with the classical first-order case. We characterize both…
In the first part of the paper, we study conformal groups that act properly discontinuously and cocompactly on simply connected, non-flat homogeneous plane waves. We show that proper cocompact similarity actions that are not isometric can…
In this note, we lay the groundwork for a new approach to the problem of group-signature classification of group actions on closed Riemann surfaces. This new approach first focuses on analyzing the low level arithmetic conditions on…
This lecture note starts with a pedagogical introduction to the theoretical background and properties of perfect actions, gives some details on topology and instanton solutions and ends with a discussion on the recent developments…
We elucidate the dynamics of ongoing collective action among intentional agents with diverse beliefs and imperfect information. Their decisions on whether or not to contribute to the collective good depend not only on the past but also on…
This is a survey on upper and lower bounds for finite group actions on bounded surfaces, 3-dimensional handlebodies and closed handles, handlebodies in arbitrary dimensions and finite graphs (the common feature of these objects is that all…
We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…