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 "Quasiconvexity and Dehn filling"

In this series we will introduce and discuss new preprints that are somehow related to the topics of the programme “Geometry at Infinity”. By incidence, this first article fits not only the topic, but also the title of this blog: the boundary at infinity. Charney, Murray: A rank-one CAT(0) group is determined by its Morse … Continue reading "A rank-one CAT(0) group is determined by its Morse boundary"