arXiv research

We prove the existence of Cannon-Thurston maps for Kleinian groups corresponding to pared manifolds whose boundary is incompressible away from cusps. We also describe the structure of these maps in terms of ending laminations.

The paper extends Euler class theory to measurable cocycles.

Stable actions of hyperbolic groups on their boundaries.

Suppose $S$ is a surface of genus $\ge 2$, $f: S \to S$ is a surface homeomorphism isotopic to a pseudo-Anosov map $α$ and suppose $\ti S$ is the universal cover of $S$ and $F$ and $A$ are lifts of $f$ and $α$ respectively. We show there is a semiconjugacy $Θ: \ti S \to \bar Ł^s \times \bar Ł^u$ from $F$ to $\bar A$, …

Study harmonic measures and rigidity in Seifert 3-manifolds using $S^1$-connections.

We give a new lower bound on the number of connected components of the space of representations of a surface group into the group of orientation preserving homeomorphisms of the circle. Precisely, for the fundamental group of a genus g surface, we show there are at least k^(2g) + 1 connected components containing repre…