Related papers: Aut(Fn) actions on representation spaces

The automorphism group $\operatorname{Aut}(F_n)$ of the free group $F_n$ acts on a space $A_d(n)$ of Jacobi diagrams of degree $d$ on $n$ oriented arcs. We study the $\operatorname{Aut}(F_n)$-module structure of $A_d(n)$ by using two…

Given a $p$-adic group $G$ equipped with an action of a finite group $\Gamma\subset\mathrm{Aut}_F(\mathbf{G})$, and a reductive fixed-point subgroup $G^\Gamma$, we establish a relationship between constructions of types for these two groups…

Let G be a finitely generated group having the property that any action of any finite-index subgroup of G by homeomorphisms of the circle must have a finite orbit. (By a theorem of E.Ghys, lattices in simple Lie groups of real rank at least…

Suppose $(X,\sigma)$ is a subshift, $P_X(n)$ is the word complexity function of $X$, and ${\rm Aut}(X)$ is the group of automorphisms of $X$. We show that if $P_X(n)=o(n^2/\log^2 n)$, then ${\rm Aut}(X)$ is amenable (as a countable,…

We implement GAP functions about groups with action on itself and investigate some basic properties of small groups with action on itself of order $<32$.

Let $G$ be a finite $p$-group and let Aut$(G)$ denote the full automorphism group of $G$. In the recent past, there has been interest in finding necessary and sufficient conditions on $G$ such that certain subgroups of Aut$(G)$ are equal.…

We study compact complex manifolds $M$ admitting a conformal holomorphic Riemannian structure invariant under the action of a complex semi-simple Lie group $G$. We prove that if the group $G$ acts transitively and essentially, then $M$ is…

Let G be a locally compact group acting properly by type-preserving automorphisms on a locally finite thick Euclidean building $\Delta$ and K be the stabilizer of a special vertex in $\Delta$. It is known that (G, K) is a Gelfand pair as…

In this paper we survey some recent results on actions of finite groups on topological manifolds. Given an action of a finite group $G$ on a manifold $X$, these results provide information on the restriction of the action to a subgroup of…

We give some natural conditions on actions of discrete countable groups on abelian locally compact groups of Lie type that imply factoriality of the group von Neumann algebras of their semidirect products. This allows us to give a fairly…

We present results on simplifying an acting group preserving properties of actions: transitivity, being a coset space and preserving a fixed equiuniformity in case of a $G$-Tychonoff space.

Let $\mathcal{C}$ be a conjugacy class of involutions in a group $G$. We study the graph $\Gamma(\mathcal{C})$ whose vertices are elements of $\mathcal{C}$ with $g,h\in\mathcal{C}$ connected by an edge if and only if $gh\in\mathcal{C}$. For…

Let $G$ be a semisimple algebraic group whose decomposition into a product of simple components does not contain simple groups of type $A$, and $P\subseteq G$ be a parabolic subgroup. Extending the results of Popov [7], we enumerate all…

In this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real…

We prove a Tits alternative theorem for groups acting on CAT(0) cubical complexes. Namely, suppose that $G$ is a group for which there is a bound on the orders of its finite subgroups. We prove that if $G$ acts properly on a…

In this article we study the automorphism group ${\rm Aut}(X,\sigma)$ of subshifts $(X,\sigma)$ of low word complexity. In particular, we prove that Aut$(X,\sigma)$ is virtually $\mathbb{Z}$ for aperiodic minimal subshifts and certain…

We investigate the configuration where a group of finite Morley rank acts definably and generically $m$-transitively on an elementary abelian $p$-group of Morley rank $n$, where $p$ is an odd prime, and $m\geqslant n$. We conclude that…

For $n>2$, given $\phi_1,...,\phi_n$ randomly chosen isometries of $S^2$, it is well-known that the group $\G$ generated by $\phi_1,...,\phi_n$ acts ergodically on $S^2$. It is conjectured in \cite{GJS} that for almost every choice of…

We study the actions of a Lie group $G$ by birationally extendible automorphisms on a domain $D\subset C^n$. For a large class of such domains defined by polynomial inequalities, all automorphisms are of this type. In the cases 1) $G$ has…

H\"older's theorem states that any group acting freely by circle homeomorphisms is abelian, this is no longer true for interval exchange transformations: we first give examples of free actions of non abelian groups. Then after noting that…