Disjoint spine phenomena in certain contractible n-manifolds (n⩾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...

Contractible n-Manifolds and the Double n-Space Property

CONTRACTIBLE n-MANIFOLDS AND THE DOUBLE n-SPACE PROPERTY

Cartesian Products of Contractible Open Manifolds

KNOTTED CONTRACTIBLE 4-MANIFOLDS IN S4 W.B.R. Lickorish

A construction will here be described that can produce a compact contractible 4-manifold M embedded piecewise linearly (or smoothly) in S4 with the fundamental group of its complement being nontrivial. Then, another embedding of M in S4 will be produced which has simply connected complement. Several examples of this will be given. Of course, the construction emphasizes that contractible spaces ...

On Covering Translations and Homeotopy Groups of Contractible Open N-manifolds

This paper gives a new proof of a result of Geoghegan and Mihalik which states that whenever a contractible open n-manifold W which is not homeomorphic to Rn is a covering space of an n-manifold M and either n ≥ 4 or n = 3 and W is irreducible, then the group of covering translations injects into the homeotopy group of W .