Compact manifolds in hyperbolicity

Horospheres and hyperbolicity of Hadamard manifolds

Article history: Available online 4 March 2014 Communicated by O. Kowalski MSC: primary 53C20 secondary 32Q05, 53C40, 53C25

Stable Manifolds under Very Weak Hyperbolicity Conditions

We present an argument for proving the existence of local stable and unstable manifolds in a general abstract setting and under very weak hyperbolicity conditions.

Surgery on Compact Manifolds

Volumes of Compact Manifolds

We present a systematic calculation of the volumes of compact manifolds which appear in physics: spheres, projective spaces, group manifolds and generalized flag manifolds. In each case we state what we believe is the most natural scale or normalization of the manifold, that is, the generalization of the unit radius condition for spheres. For this aim we first describe the manifold with some pa...

Aspherical Manifolds, Relative Hyperbolicity, Simplicial Volume, and Assembly Maps

This paper contains examples of closed aspherical manifolds obtained as a by-product of recent work by the author [Bel] on the relative strict hyperbolization of polyhedra. The following is proved. (I) Any closed aspherical triangulated n-manifold M with hyperbolic fundamental group is a retract of a closed aspherical triangulated (n+ 1)manifold N with hyperbolic fundamental group. (II) If B1, ...