Interiors of compact contractible a-manifolds are hyperbolic (N ≥ 5)

Abstract

The interior of every compact contractible PL n-manifold (n ≥ 5) supports a complete geodesic metric of strictly negative curvature. This provides a new family of simple examples illustrating the negative answer to a question of M. Gromov which asks whether metrically convex geodesic spaces which are topological manifolds must be homeomorphic to Euclidean spaces. The first examples verifying the negative answer to this question were given by M. Davis and T. Januszkiewicz [11]. © 1997 J. differential geometry.