Hyperbolic manifolds as codimension-1 and -2 complements
by
Dubravko Ivanšić
University of Oklahoma

We consider the question of when a finite-volume hyperbolic (n+1)-manifold M may be embedded as a complement of a closed codimension-k submanifold A inside a closed (n+1)-manifold N. We show that if this is possible, then every flat manifold E corresponding to an end of M is either an S⁰ or S¹-bundle, giving that k is either 1 or 2. We give a criterion in terms of the fundamental group when E is an S¹ bundle, which is used to tell when M is a codimension-2 complement. Furthermore, we show that there are at most finitely many 4-manifolds M so that M=S⁴-{tori \cup Klein bottles}. If M is a codimension-1 complement, we show that the universal cover of N is \rnp and, with an additional assumption, there are only finitely many choices for N in dimensions n=2, 3.

Date received: May 21, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabi-08.