Precompactness for finite volume negatively curved manifolds
by
Igor Belegradek
McMaster University

We prove a finiteness theorem for finite volume negatively curved manifolds that can be thought of as a variable curvature version of Mostow Rigidity. Namely, let M(a, b, n, G) be the class of finite volume complete Riemannian n-manifolds with sectional curvatures within [a, b] and with fundamental groups isomorphic to G. Then, if n > 2 and a <= b < 0, the class M(a, b, n, G) is precompact in pointed C^{1, \alpha} topology. In particular, many metric invariants of manifolds in M(a, b, n, G) vary within fixed bounds. Furthermore, M(a, b, n, G) breaks into finitely many diffeomorphism classes. The key lemma needed is that G does not split over a virtually nilpotent subgroup.

http://icarus.math.mcmaster.ca/belegi/belegi.html

Date received: January 9, 1999

Copyright © 1999 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 # caca-05.