Interiors of compact contractible $n$-manifolds are hyperbolic $(n\geq 5)$

Interiors of Compact Contractible N-manifolds Are Hyperbolic (n 5)

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 rst examples verifying the ne...

Compact Hyperbolic 4-manifolds of Small Volume

We prove the existence of a compact non-orientable hyperbolic 4-manifold of volume 32π2/3 and a compact orientable hyperbolic 4-manifold of volume 64π2/3, obtainable from torsion-free subgroups of small index in the Coxeter group [5, 3, 3, 3]. At the time of writing these are the smallest volumes of any known compact hyperbolic 4-manifolds.

Contractible n-Manifolds and the Double n-Space Property

CONTRACTIBLE n-MANIFOLDS AND THE DOUBLE n-SPACE PROPERTY

Deformation Spaces Associated to Compact Hyperbolic Manifolds

Recently, there has been considerable interest in spaces of locally homogeneous (or geometric) structures on smooth manifolds, motivated by Thurston [6, 7]. If M is a smooth manifold, we will let C(M) denote the space of conformai structures (with marking) on M and P(M) the space of projective structures (with marking) on M. Since these spaces are a measure of the complexity of the fundamental ...

Contractible Open 3-manifolds Which Non-trivially Cover Only Non-compact 3-manifolds