Geometric boundaries of hyperbolic manifolds
This talk will address various questions concerning when flat n-manifolds
or hyperbolic n-manifolds bound a hyperbolic (n+1)-manifold.
More precisely, we consider the question of whether every flat n-manifold
is, up to diffeomorphism, a cusp cross-section of a complete finite volume
1-cusped hyperbolic (n+1)-manifold. We also discuss the question
of whether a closed orientable hyperbolic
n-manifold can be the
totally geodesic boundary of a compact complete hyperbolic (n+1)-manifold.
We will show the answers to both these questions are no.
Spring 2001 meeting of the PNGS