Related papers: Free actions on handlebodies

We examine free orientation-reversing group actions on orientable handlebodies, and free actions on nonorientable handlebodies. A classification theorem is obtained, giving the equivalence classes and weak equivalence classes of free…

In this paper we consider all orientation-preserving $\mathbb{Z}_{4}$-actions on $3$-dimensional handlebodies $V_g$ of genus $g>0$. We study the graph of groups $(\Gamma($v$),\mathbf{G(v)})$, which determines a handlebody orbifold…

Fix a free, orientation-preserving action of a finite group G on a 3-dimensional handlebody V. Whenever G acts freely preserving orientation on a connected 3-manifold X, there is a G-equivariant imbedding of V into X. There are choices of X…

In this paper we consider all orientation-preserving $\mathbb{Z}_{p^2}$-actions on 3-dimensional handlebodies $V_g$ of genus $g>0$ for $p$ an odd prime. To do so, we examine particular graphs of groups $(\Gamma($v$),\mathbf{G(v)})$ in…

We show that if a countable group $G$ is the free product of infinite abelian groups, then for every free, probability-measure-preserving (p.m.p.) action of $G$, its orbit equivalence class is weakly dense in the space of p.m.p. actions of…

It is proven that the orbit-equivalence class of any essentially free probability-measure-preserving action of a free group $G$ is weakly dense in the space of actions of $G$.

We consider finite group-actions on closed, orientable and nonorientable 3-manifolds; such a finite group-action leaves invariant the two handlebodies of a Heegaard splitting of M of some genus g. The maximal possible order of a finite…

Let $\widetilde{S}$ be a closed (compact without boundary) oriented surface with genus $g$, and $G$ be a group isomorphic to $% \mathbf{Z}_{p}^{m}$, where $p$ is a prime integer. An action of $G$ on $S$ is a pair $(\widetilde{S},f)$, where…

For a group $G$ generated by $k$ elements, the Nielsen equivalence classes are defined as orbits of the action of $\operatorname{Aut} F_k$, the automorphism group of the free group of rank $k$, on the set of generating $k$-tuples of $G$.…

Suppose $G$ is a $\mathcal{T}$-group (finitely generated torsion-free nilpotent) with centralizers outside of the derived subgroup being abelian of rank equal to $\text{rank}(Z_1)+1$. This includes the class of free nilpotent groups…

Let $V$ be a connected $3$-dimensional handlebody of finite genus at least $3$. We prove that the handlebody group $\mathrm{Mod}(V)$ is superrigid for measure equivalence, i.e. every countable group which is measure equivalent to…

We use the notion of fixity for representations of finite groups to construct free and smooth actions on products of spheres. In particular we show that a finite p-group (for p>3) will act freely and smoothly on a product of two spheres if…

We consider finite group-actions on closed, orientable and nonorientable 3-manifolds M which preserve the two handlebodies of a Heegaard splitting of M of some genus g > 1 (maybe interchanging the two handlebodies). The maximal possible…

We show that for every $n\ge 2$ there exists a torsion-free one-ended word-hyperbolic group $G$ of rank $n$ admitting generating $n$-tuples $(a_1,\ldots ,a_n)$ and $(b_1,\ldots ,b_n)$ such that the $(2n-1)$-tuples $$(a_1,\ldots ,a_n,…

This paper focuses on the classification of classes of topological equivalence of finite group actions on Riemann surfaces. By the Riemann-Hurwitz bound, there are just finitely many groups that act conformally on a closed orientable…

If G is a finitely generated powerful pro-p group satisfying a certain law v=1, and if G can be generated by a normal subset T of finite width which satisfies a positive law, we prove that G is nilpotent. Furthermore, the nilpotency class…

We show that a free action $G \curvearrowright X$ is almost finite if its restriction to some infinite normal subgroup of $G$ is almost finite. Consider the class of groups which contains all infinite groups of locally subexponential growth…

Let p be a prime and G be a torsion-free abelian group. A homomorphism from G to the p-adic integers is called a p-adic functional on G. If G has finite rank, then G can be represented as an inductive limit of an inductive sequence of free…

We extend Dye's reconstruction theorem, which classifies isomorphisms between full groups, to a classification of homomorphisms between full groups. For full groups of ergodic p.m.p. equivalence relations, our result roughly says that such…

The classifying spaces of handlebody groups form a modular operad. Algebras over the handlebody operad yield systems of representations of handlebody groups that are compatible with gluing. We prove that algebras over the modular operad of…