13 citations · 59 across the 34 of their papers we have counts for
9 papers · 1 filter
Obstructions to nonpositive curvature for open manifolds
Igor Belegradek
We study algebraic conditions on a group G under which every properly discontinuous, isometric G-action on a Hadamard manifold has a G-invariant Busemann function. For such G we pr…
Hyperplane arrangements in negatively curved manifolds and relative hyperbolicity
Igor Belegradek, G. Christopher Hruska
We show that certain aspherical manifolds arising from hyperplane arrangements in negatively curved manifolds have relatively hyperbolic fundamental group.
Complex hyperbolic hyperplane complements
Igor Belegradek
We study spaces obtained from a complete finite volume complex hyperbolic n-manifold M by removing a compact totally geodesic complex (n-1)-submanifold. The main result is that the…
Rigidity and relative hyperbolicity of real hyperbolic hyperplane complements
Igor Belegradek
For n>3 we study spaces obtained from finite volume complete real hyperbolic n-manifolds by removing a compact totally geodesic submanifold of codimension two. We prove that their…
Rips construction and Kazhdan property (T)
Igor Belegradek, Denis Osin
We show that for any non--elementary hyperbolic group and any finitely presented group , there exists a short exact sequence , where is a hyperbol…
Aspherical manifolds, relative hyperbolicity, simplicial volume and assembly maps
Igor Belegradek
This paper contains examples of closed aspherical manifolds obtained as a by-product of recent work by the author [arXiv:math.GR/0509490] on the relative strict hyperbolization of…