Related papers: The modular action on PSL(2,R)-characters in genus…

In this paper we consider the action of the mapping class group of a surface on the space of homomorphisms from the fundamental group of a surface into PSL(2,R). Goldman conjectured that when the surface is closed and of genus bigger than…

We prove that in genus bigger than $2$, the mapping class group action on $\mathrm{Aff}(\mathbb{C})$-characters is ergodic. This implies that almost every representation $\pi_1 S \longrightarrow \mathrm{Aff}(\mathbb{C})$ is the holonomy of…

Let S be a compact orientable surface with genus g and n boundary components d_1,...,d_n. Let b = (b_1, ..., b_n) where b_n lies in [-2,2]. Then the mapping class group of S acts on the relative SU(2)-character variety X comprising…

Let $\Sigma$ be a compact orientable surface of genus $g=1$ with $n=1$ boundary component. The mapping class group $\Gamma$ of $\Sigma$ acts on the SU(3)-character variety of $\Sigma$. We show that the action is ergodic with respect to the…

This note investigates the dynamics of the mapping class group action on the character variety of super-maximal representations of the fundamental group of a punctured sphere into $\text{PSL}(2,\mathbb{R})$, discovered by Deroin and…

In this article, we continue the study of the action of subgroups of the mapping class group on the $SU(2)$-character variety. We prove the existence of a mapping class subgroup on the surface of genus $2$, containing infinitely many…

We study the action of the mapping class group Mod(S) on the boundary dQ of quasifuchsian space Q. Among other results, Mod(S) is shown to be topologically transitive on the subset C in dQ of manifolds without a conformally compact end. We…

We prove some ergodic-theoretic rigidity properties of the action of SL(2,R) on moduli space. In particular, we show that any ergodic measure invariant under the action of the upper triangular subgroup of SL(2,R) is supported on an…

The purpose of this paper is to study the action of the mapping class group on the moduli space of representations of the fundamental group of a non-orientable surface into SU(2). The action is shown to be ergodic with respect to a natural…

For n>2, the action of the outer automorphism group of the rank n free group F_n on the SU(2)-character variety Hom(F_n,SU(2))/SU(2)$ is ergodic with respect to the Lebesgue measure class.

The group Gamma of automorphisms of the polynomial kappa(x,y,z) = x^2 + y^2 + z^2 - xyz -2 is isomorphic to PGL(2,Z) semi-direct product with (Z/2+Z/2). For t in R, Gamma-action on ktR = kappa^{-1}(t) intersect R displays rich and varied…

The aim of this article is to prove that the Torelli group action on the G-character varieties is ergodic for G a connected, semi-simple and compact Lie group.

We prove that the mapping class group of a closed surface acts ergodically on connected components of the representation variety corresponding to a connected compact Lie group.

We describe the orbits of the irreducible action of PSL(2, R) on the 3-dimensional Einstein universe Ein 1,2. This work completes the study in [2], and is one element of the classification of cohomo-geneity one actions on Ein 1,2 ([5]).

Let $e$ denote the Euler class on the space $Hom(\Gamma_g, PSL(2,\mathbb R))$ of representations of the fundamental group $\Gamma_g$ of the closed surface $\Sigma_g$ of genus $g$. Goldman showed that the connected components of…

The mapping class group of a compact oriented surface of genus greater than one with boundary acts ergodically on connected components of the representation variety corresponding to a connected compact Lie group, for every choice of…

Among the ergodic actions of a compact quantum group $\mathbb{G}$ on possibly non-commutative spaces, those that are {\it embeddable} are the natural analogues of actions of a compact group on its homogeneous spaces. These can be realized…

We study the relative SU(2,1)-character varieties of the one-holed torus, and the action of the mapping class group on them. We use an explicit description of the character variety of the free group of rank two in SU(2,1) in terms of…

We study the action of G = SL(2,R) on its type space S_G(R) where R denotes the field of real numbers. We identify a minimal closed G-flow I, and an idempotent r of I (with the respect to the Ellis semigroup structure * on I). We show that…

We study the symplectic geometry of the SU(2)-representation variety of the compact oriented surface of genus 2. We use the Goldman flows to identify subsets of the moduli space with corresponding subsets of $\mathbb P^3(\mathbb C)$. We…