9 papers
Nonnegative curvature, symmetry and fundamental group
Igor Belegradek
We prove a result on equivariant deformations of flat bundles, and as a corollary, we obtain two ``splitting in a finite cover'' theorems for isometric group actions on Riemannian…
On co-Hopfian nilpotent groups
Igor Belegradek
We characterize co-Hopfian finitely generated torsion free nilpotent groups in terms of their Lie algebra automorphisms, and construct many examples of such groups.
Pinching surface groups in complex hyperbolic plane
Igor Belegradek
We construct first examples of discrete geometrically finite subgroups of PU(2,1) which contain parabolic elements, and are isomorphic to surface groups.
Vector bundles with infinitely many souls
Igor Belegradek
We construct the first examples of manifolds, the simplest one being the product of S^3, S^4, and R^5, which admit infinitely many complete nonnegatively curved metrics with pairwi…
Metrics of positive Ricci curvature on vector bundles over nilmanifolds
Igor Belegradek, Guofang Wei
We construct metrics of positive Ricci curvature on some vector bundles over tori (or more generally, over nilmanifolds). This gives rise to the first examples of manifolds with po…
On Mostow rigidity for variable negative curvature
Igor Belegradek
We prove a finiteness theorem for the class of complete finite volume Riemannian manifolds with pinched negative sectional curvature, fixed fundamental group, and of dimension …