Josh Barnard's Research

My research area is geometric group theory, mostly the behavior of surface groups in negatively and postively curved groups. Listed below are publications and preprints, in roughly reverse chronological order. Click or scroll down for abstracts and files.

[Mathematical notation on this page is rendered using MathJax.]
[Page format shamelessly stolen from Matt Clay.]

In Progress
Graph small cancellation groups are automatic (with Trey Trampel)

Preprints
On tameness of surface actions on Gromov hyperbolic 3-manifolds
Bounding surface actions on hyperbolic spaces II
Geometrically infinite surfaces in 3-manifolds with hyperbolic fundamental group

Publications
Bounding surface actions on hyperbolic spaces, Geometriae Dedicata.
A loop theorem/Dehn's lemma for some orbifolds, Algebraic & Geometric Topology, 11 (2011), 2815-2827.
Super-exponential 2-dimensional Dehn functions, to appear in Groups, Geometry, and Dynamics.
Super-exponential distortion of subgroups of CAT(-1) groups, Algebraic & Geometric Topology, 7 (2007), 301-308.
Distortion of surface groups in CAT(0) free-by-cyclic groups, Geometriae Dedicata, 120 (2006), no. 1, 119-139.

Thesis
Ends of word-hyperbolic three-manifolds, PhD thesis (2004)