Compact, contractible $n$-manifolds and their boundaries.

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 manifolds with computable boundaries

We investigate conditions under which a co-computably enumerable closed set in a computable metric space is computable and prove that in each locally computable computable metric space each co-computably enumerable compact manifold with computable boundary is computable. In fact, we examine the notion of a semi-computable compact set and we prove a more general result: in any computable metric ...

Contractible n-Manifolds and the Double n-Space Property

CONTRACTIBLE n-MANIFOLDS AND THE DOUBLE n-SPACE PROPERTY

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

Degree theory and BMO; part I: Compact manifolds without boundaries

In this paper we consider degree theory for mappings u from one compact smooth n-dimensional manifold X to a connected compact smooth manifold Y of the same dimension. These are manifolds without boundary and which are oriented. The classical degree counts the "number of times" Y is covered by u(X), taking into account algebraic multiplicity. For instance, if u E C 1 and y E Y is a regular valu...