Related papers: Orbital Counting in Conjugacy Classes

Given a discrete group $\Gamma$ of isometries of a negatively curved manifold $\widetilde M$, a nontrivial conjugacy class $\mathfrak K$ in $\Gamma$ and $x_0\in\widetilde M$, we give asymptotic counting results, as $t\to +\infty$, on the…

In this paper we study the action of the fundamental group of a finite metric graph on its universal covering tree. We assume the graph is finite, connected and the degree of each vertex is at least three. Further, we assume an…

Let G be a group and let M be a CAT(0) proper metric space (e.g. a simply connected complete Riemannian manifold of non-positive sectional curvature or a locally finite tree). Isometric actions of G on M are (by definition) points in the…

In this paper, we establish statistical results for a convex co-compact action of a free group on a CAT($-1$) space where we restrict to a non-trivial conjugacy class in the group. In particular, we obtain a central limit theorem where the…

We introduce and study the notion of continuous orbit equivalence of actions of countable discrete groups on Cartan pairs in (twisted) groupoid context. We characterize orbit equivalence of actions in terms of the corresponding…

We describe a cocompact model for the classifying space for proper actions of the mapping class group of a surface with punctures and boundary components. Our construction relies on a known model for the case of a closed surface and uses an…

Let $M$ be a compact closed manifold of variable negative curvature. Fix an element $\operatorname{id} \neq \gamma$ in the fundamental group $\Gamma$ of $M$, and denote the set of elements in $\Gamma$ that are conjugate to $\gamma$ by…

The relation between fixed point and orbit count sequences is investigated from the point of view of linear mappings on the space of arithmetic functions. Spectral and asymptotic properties are derived and several quantities are explicitly…

For an action of the circle group $S^1$ on a compact oriented manifold with isolated fixed points, there is a claim that weights at the fixed points occur in pairs. This phenomenon holds for other types of $S^1$-manifolds, e.g., (almost)…

We classify generic coadjoint orbits for symplectomorphism groups of compact symplectic surfaces with or without boundary. We also classify simple Morse functions on such surfaces up to a symplectomorphism.

Let G be a real compact connected simple Lie group, and g its Lie algebra. We study the problem of determining, from root data, when a sum of adjoint orbits in g, or a product of conjugacy classes in G, contains an open set. Our general…

We consider asymptotic orbit-counting problems for certain expansive actions by commuting automorphisms of compact groups. A dichotomy is found between systems with asymptotically more periodic orbits than the topological entropy predicts,…

We consider several weaker versions of the notion of conjugacy and orbit equivalence of measure preserving actions of countable groups on probability spaces, involving equivalence of the ultrapower actions and asymptotic intertwining…

In this paper we study topological rigidity of affine actions on compact connected metrizable abelian groups. We also classify one-parameter flows of translations upto orbit equivalence and discrete group actions by translations upto…

In this paper, we consider semigroup actions of discrete countable semigroups on compact spaces by surjective local homeomorphisms. We introduce notions of continuous one-sided orbit equivalence and continuous orbit equivalence for…

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…

In this paper, we derive an asymptotic formula for the number of conjugacy classes of elements in a class of statistically convex-cocompact actions with contracting elements. Denote by $\mathcal C(o, n)$ (resp. $\mathcal C'(o, n)$) the set…

We study closures of conjugacy classes in the symmetric matrices of the orthogonal group and we determine which one are normal varieties. In contrast to the result for the symplectic group where all classes have normal closure, there is…

We study the topology of compact manifolds with a Lie group action for which there are only finitely many non-principal orbits, and describe the possible orbit spaces which can occur. If some non-principal orbit is singular, we show that…

We compute the mapping class group orbits in the homotopy set of framings of a compact connected oriented surface with non-empty boundary. In the case $g > 1$ the computation is some modification of Johnson's results and certain arguments…