Related papers: Free subgroups acting properly discontinuously

Let G be a one-ended group acting discretely and co-compactly on a CAT(0) space X. We show that the boundary of X has no cut points and that one can detect splittings of $G$ over two-ended groups and recover its JSJ decomposition from the…

Let $X$ be a $2n$-manifold with a locally standard action of a compact torus $T^n$. If the free part of action is trivial and proper faces of the orbit space $Q$ are acyclic, then there are three types of homology classes in $X$: (1)…

Let $G$ be a compact Hausdorff topological group acting on a compact Hausdorff topological space $X$. Within the $C^{*}$-algebra $C(X)$ of all continuous complex-valued functions on $X$, there is the Peter-Weyl algebra $\mathcal{P}_G(X)$…

The result often known as Joiner's lemma is fundamental in understanding the topology of the free topological group $F(X)$ on a Tychonoff space$X$. In this paper, an analogue of Joiner's lemma for the free paratopological group $\FP(X)$ on…

A group action is said to be highly-transitive if it is $k$-transitive for every $k \ge 1$. The main result of this thesis is the following: Main Theorem: The fundamental group of a closed, orientable surface of genus > 1 admits a…

A discrete subset $S$ of a topologically gyrogroup $G$ is called a {\it suitable set} for $G$ if $S\cup \{1\}$ is closed and the subgyrogroup generated by $S$ is dense in $G$, where $1$ is the identity element of $G$. In this paper, we…

Let $C_2$ denote the cyclic group of order 2. We compute the $RO(C_2)$-graded cohomology of all $C_2$-surfaces with constant integral coefficients. We show when the action is nonfree, the answer depends only on the genus, the orientability…

Let G be a simple non-compact linear connected Lie group and H be a closed non-compact semisimple subgroup. We are interested in finding classes of homogeneous spaces G/H admitting proper actions of discrete non virtually abelian subgroups…

Let $G$ be a Lie group, $\Gamma\subset G$ a discrete subgroup, $X=G/\Gamma$, and $f$ an affine map from $X$ to itself. We give conditions on a submanifold $Z$ of $X$ guaranteeing that the set of points $x\in X$ with $f$-trajectories…

We give a systematic treatment of the stability theory for action of a real reductive Lie group G on a topological space. More precisely, we introduce an abstract setting for actions of non-compact real reductive Lie groups on topological…

Let $G$ be a connected Lie group and $\text{Sub}_G$ be the space of closed subgroups of $G$ equipped with the Chabauty topology. In this article, we investigate the existence of invariant random subgroups of $G$ supported on various orbits…

We study actions of discrete groups on contractible topological spaces in which either (1) all stabilizers lie in the family of subgroups of prime power order or (2) all stabilizers lie in the family of finite subgroups. We compare the…

The topological data of a group action on a compact Riemann surface is often encoded using a tuple $(h;m_1,\dots ,m_s)$ called its signature. There are two easily verifiable arithmetic conditions on a tuple necessary for it to be a…

For a discrete metric space (or more generally a large scale space) $X$ and an action of a group $G$ on $X$ by coarse equivalences, we define a type of coarse quotient space $X_G$, which agrees up to coarse equivalence with the orbit space…

We show that the topological rank of an orbit full group generated by an ergodic, probability measure-preserving free action of a non-discrete unimodular locally compact Polish group is two. For this, we use the existence of a cross section…

The shadowable points of dynamical systems has been well-studied by Morales \cite{MR3535492}. This paper aims to generalize the main results obtained by Morales to free semigroup actions. To this end, we introduce the notion of shadowable…

In this paper we give sufficient conditions under which a subsemigroup of a topological group is a subgroup, adding to the results given in \cite{Kosh, can, axioms, forum, Hof, cc, locally} where conditions exist (such as locally…

If a Lie group acts on a manifold freely and properly, pulling back by the quotient map gives an isomorphism between the differential forms on the quotient manifold and the basic differential forms upstairs. We show that this result remains…

We define two complexes on which the group Aut$(F_n)$ acts freely. The homotopy groups of these are studied. They map to the K-groups of Z and are themselves a sort of pre-K-theory.

We provide an algorithm that, given a finite set of generators for a subgroup $H$ of a finitely generated free group $F$, determines whether $H$ is echelon or not and, in case of affirmative answer, also computes a basis with respect to…