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- Igor Belegradek, Andrzej Szczepanski
- IJAC
- 2008

We generalize some results of Paulin and Rips-Sela on endomorphisms of hyperbolic groups to relatively hyperbolic groups, and in particular prove the following. â€¢ If G is a non-elementary relatively hyperbolic group with slender parabolic subgroups, and either G is not co-Hopfian or Out(G) is infinite, then G splits over a slender group. â€¢ If H is aâ€¦ (More)

- Igor Belegradek, VITALI KAPOVITCH
- 2000

According to the soul theorem of J. Cheeger and D. Gromoll [CG72], a complete open manifold of nonnegative sectional curvature is diffeomorphic to the total space of the normal bundle of a compact totally geodesic submanifold, called the soul. A natural problem is to what extent the converse to the soul theorem holds. In other words, one asks which vectorâ€¦ (More)

- Igor Belegradek, VITALI KAPOVITCH
- 2004

We give a diffeomorphism classification of pinched negatively curved manifolds with amenable fundamental groups, namely, they are precisely the MÃ¶bius band, and the products of R with the total spaces of flat vector bundles over closed infranilmanifolds.

We construct new examples of manifolds of positive Ricci curvature which, topologically, are vector bundles over compact manifolds of almost nonnegative Ricci curvature. In particular, we prove that if E is the total space of a vector bundle over a compact manifold of nonnegative Ricci curvature, then E Ã— R admits a complete metric of positive Ricciâ€¦ (More)

- Igor Belegradek, VITALI KAPOVITCH
- 2000

We prove several finiteness theorems for the normal bundles to souls in nonnegatively curved manifolds. More generally, we obtain finiteness results for open Riemannian manifolds whose topology is concentrated on compact domains of â€œbounded geome-

- Igor Belegradek
- 2008

We characterize co-Hopfian finitely generated torsion free nilpotent groups in terms of their Lie algebra automorphisms, and construct many examples of such groups.

- Igor Belegradek
- 2000

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 â‰¥ 3. One of the key ingredients is that the fundamental group of such a manifold does not admit a small nontrivial action on an R -tree.

- Igor Belegradek
- 2008

We show that the aspherical manifolds produced via the relative strict hyperbolization of polyhedra enjoy many group-theoretic and topological properties of open finite volume negatively pinched manifolds, including relative hyperbolicity, nonvanishing of simplicial volume, co-Hopf property, finiteness of outer automorphism group, absence of splitting overâ€¦ (More)

- Igor Belegradek
- 2003

We construct the first examples of manifolds, the simplest one being S3Ã—S4Ã—R5, which admit infinitely many complete nonnegatively curved metrics with pairwise nonhomeomorphic souls. According to the soul theorem of J. Cheeger and D. Gromoll [CG72], a complete open manifold of nonnegative sectional curvature is diffeomorphic to the total space of the normalâ€¦ (More)

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 positive Ricci curvature which are homotopy equivalent but not homeomorphic to manifolds of nonnegative sectional curvature.