Related papers: Imbeddings of free actions on handlebodies

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…

A group action H on X is called "telescopic" if for any finitely presented group G, there exists a subgroup H' in H such that G is isomorphic to the fundamental group of X/H'. We construct examples of telescopic actions on some CAT[-1]…

We describe a procedure to deform cubulations of hyperbolic groups by "bending hyperplanes". Our construction is inspired by related constructions like Thurston's Mickey Mouse example, walls in fibred hyperbolic $3$-manifolds and…

Assume that M is a closed hyperbolic 3-manifold fibering over the circle with fiber a closed orientable surface of genus g. We show that if M has large diameter and its injectivity radius is bounded below, then the rank of the fundamental…

In this paper we present a new characterization of free group actions (in classical differential geometry), involving dynamical systems and representations of the corresponding transformation groups. In fact, given a dynamical system, we…

We give a necessary and sufficient condition for a simple closed curve on the boundary of a genus two handlebody to decompose the handlebody into (torus with one boundary component times [0,1]. We use this condition to decide whether a…

We show that conservative partially hyperbolic diffeomorphism isotopic to the identity on Seifert 3-manifolds are ergodic.

Let $A$ be a group isomorphic with either $S_4$, the symmetric group on four symbols, or $D_8$, the dihedral group of order 8. Let $V$ be a normal four-subgroup of $A$ and $\alpha$ an involution in $A\setminus V$. Suppose that $A$ acts on a…

For the oriented 3-dimensional handlebody constructed from a 3-ball by attaching g 1-handles, it is shown that the natural surjection from the group of orientation preserving diffeomorphisms of it to the mapping class group of it has no…

We establish a 3-manifold invariant for each finite-dimensional, involutory Hopf algebra. If the Hopf algebra is the group algebra of a group $G$, the invariant counts homomorphisms from the fundamental group of the manifold to $G$. The…

We consider knots and links in handlebodies that have hyperbolic complements and operations akin to composition. Cutting the complements of two such open along separating twice-punctured disks such that each of the four resulting…

A random group contains many subgroups which are isomorphic to the fundamental group of a compact hyperbolic 3-manifold with totally geodesic boundary. These subgroups can be taken to be quasi-isometrically embedded. This is true both in…

We prove several results asserting that the action of a Banach-Lie group on Hilbert spaces of holomorphic sections of a holomorphic Hilbert space bundle over a complex Banach manifold is multiplicity free. These results require the…

Let X/S be a semistable curve with an action of a finite group G and let H be a normal subgroup of G. We present a new condition under which for any base change T->S, (X/G)*T is isomorphic to (X*T)/G. This allows us to define induction and…

Suppose a finite group $G$ acts on a manifold $M$. By a theorem of Mostow, also Palais, there is a $G$-equivariant embedding of $M$ into the $m$-dimensional Euclidean space $\RR^{m}$ for some $m$. We are interested in some explicit bounds…

The orbit polytope for a finite group G acting linearly and freely on a sphere S is used to construct a cellularized fundamental domain for the action. A resolution of the integers over G results from the associated G-equivariant…

We study two actions of big mapping class groups. The first is an action by isometries on a Gromov-hyperbolic graph. The second is an action by homeomorphisms on a circle in which the vertices of the graph naturally embed. The first two…

Let G be the Heisenberg group of real lower triangular 3x3 matrices with unit diagonal. A locally free smooth action of G on a manifold M^4 is given by linearly independent vector fields X_1, X_2, X_3 such that X_3 = [X_1,X_2] and [X_1,X_3]…

This article studies connections between group actions and their corresponding vector spaces. Given an action of a group $G$ on a nonempty set $X$, we examine the space $L(X)$ of scalar-valued functions on $X$ and its fixed subspace: $$…

A group of bijections G acting on a set X is said with fixed points (abbreviated as gaf from the french "groupe {\`a} points fixes") if any element of G has at least one fixed point in X. The G group is said with a common fixed point…