
Abstract. We show that any simplicial free action of the fundamental group of a closed hyperbolic surface on a contractible, uniformly locally finite simplicial, \(\delta\)hyperbolic 3manifold is geometrically and topologically tame. The proof is based on Bonahon's proof of geometric tameness for freely indecomposable hyperbolic 3manifolds. (3/26/13)

Abstract. Suppose \(S\) is a closed orientable surface of genus \(g\geq 2\), and that \(\pi_1(S)\) acts freely and properly discontinuously by isometries on a simply connected \(\delta\)hyperbolic pathmetric space \(X\). Suppose further that the injectivity radius of this action is bounded below by \(\epsilon>0\). There is a constant \(D\), depending only on \(\delta\), \(g\), \(\epsilon\), and \(f\), with the following property: If \(\Gamma\) is a graph that fills S and has \(f\) complementary components, then there is a map \(\varphi:S\to X/\pi_1(S)\), inducing the natural isomorphism on fundamental groups, such that the image of \(\Gamma\) has total length no more than \(D\). (3/14/13)

Abstract. Given an isometric action of the fundamental group of a closed orientable surface on a deltahyperbolic space, we find a standard generating set whose translation distances are bounded above in terms of the hyperbolicity constant delta, the genus of the surface, and the injectivity radius of the action, which we assume to be strictly positive. 
Abstract. The equivariant loop theorem implies the existence of a loop theorem/Dehn's lemma for threeorbifolds that are good (covered by a threemanifold). In this note we prove a loop theorem/Dehn's lemma for any locallyorientable threedimensional orbifold (good or bad) whose singular set is labeled with powers of 2. The proof is modeled on the standard tower construction. 
Abstract. We produce examples of groups of type \(\mathcal{F}_3\) with 2dimensional Dehn functions of the form exp\(^n(x)\) (a tower of exponentials of height \(n\)), where \(n\) is any natural number. 
Abstract. We construct 2dimensional CAT(1) groups which contain free subgroups with arbitrary iterated exponential distortion, and with distortion higher than any iterated exponential. 
Abstract. Given a nonpositively curved 2complex with a circlevalued Morse function satisfying some extra combinatorial conditions, we describe how to locally isometrically embed this in a larger nonpositively curved 2complex with freebycyclic fundamental group. This embedding procedure is used to produce examples of CAT(0) freebycyclic groups that contain closed hyperbolic surface subgroups with polynomial distortion of arbitrary degree. We also produce examples of CAT(0) hyperbolic freebycyclic groups that contain closed hyperbolic surface subgroups that are exponentially distorted. 
Abstract. We prove a partial generalization of Bonahon's tameness result to surfaces inside irreducible 3manifolds with hyperbolic fundamental group.
Bonahon's result states that geometrically infinite ends of freely indecomposable hyperbolic 3manifolds are simply degenerate. It is easy to see that a geometrically infinite end gives rise to a sequence of curves on the corresponding surface whose geodesic representatives are not contained in any compact set. The main step in his proof is showing that one may assume that these curves are simple on the surface. In this paper, we generalize the main step of Bonahon's proof, showing that a geometrically infinite end gives rise to a sequence of simple surface curves whose geodesic representatives are not contained in any compact set. [N.B.: This paper will not be published, as its results have been subsumed by work in progress.] 
Abstract. We show that certain surface subgroups of wordhyperbolic threemanifold groups are geometrically tame. The result applies to any surface subgroup which is bounded in a reasonable sense analogous to the way in which pleated surfaces have bounded diameter in hyperbolic threemanifolds. We conjecture that all surface subgroups of wordhyperbolic threemanifold groups satisfy this boundedness condition. In this direction, we show in the appendix that a similar, though somewhat weaker, condition is satisfied by all surface subgroups of general wordhyperbolic groups.
[N.B.: The bulk of this work is contained in the paper "Geometrically infinite surfaces in 3manifolds with hyperbolic fundamental group," while the result of the appendix is subsumed by the paper "Bounding surface actions on hyperbolic spaces," both of which are listed above.] 