Abelain 2-groups and Approximate Fibrations
by
R. J. Daverman
University of Tennessee
Coauthors: Yongkuk Kim

A closed n-manifold N is a codimension-2 fibrator if it automatically induces approximate fibrations, in the following sense: given a closed map p from an (n+2)-manifold M onto a (metric) space B such that each preimage under p is a copy of N , up to shape, p is an approximate fibration. The mail result, which answers a question posed by N. Chinen, expands the extensive list of known codimension-2 fibrators. Theorem: All closed n-manifolds N whose fundamental groups are Abelian 2-groups are codimension-2 fibrators. This constrasts neatly with recently developed examples of nonfibrators N having cyclic fundamental groups of odd order. In addition, the role of finite torsion is clarified by another result. Theorem: If G is a finitel generated, residually finite group such that G/G' is cyclic of order d yet the order of no element of G divides d , then G is hyperhopfian. Hence, every closed n-amnifold having findamental group isomorphic to G is a codimension-2 fibrator.

Date received: May 12, 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-07.