Zimmer’s conjecture aims to extend Margulis’ superrigidity theorem to a nonlinear setting. Except for actions on the circle there has not been much progress in the last 35 years. A new preprint of Brown-Fisher-Hurtado and its predecessor are now settling the conjecture for finite index subgroups of \(SL(n,{\mathbb Z})\) and cocompact lattices in \(SL(n,{\mathbb R})\). … Continue reading "What’s new on the ArXiv: Zimmer’s conjecture for actions of SL(m,Z)"

One of the most important theorems in 3-manifolds topology is Agol’s Theorem asserting that every closed 3-manifold is virtually fibered and in particular virtually Haken. Agol proved this theorem in early 2012 for closed hyperbolic manifolds. The general (closed) case reduces to hyperbolic manifolds via geometrization. The case of cusped hyperbolic manifolds was left open … Continue reading "What’s new on the ArXiv: Quasiconvexity and Dehn filling"