Fibrator Properties of Partially Aspherical Manifolds
by
Robert J. Daverman
University of Tennessee

This talk is based on joint work with Young Ho Im and Yongkuk Kim. A closed n-manifold N is a codimension-k PL fibrator in the orientable category if for each orientable (n+k)-manifold M^n+k and PL map p:M --> B to a simplicial complex B such that each p^-1(b), b in B, is a copy of N (or, more generally, collapses to an n-complex homotopy equivalent to N), the map p is an approximate fibraion. N is said to be t-aspherical if its universal cover is t-connected. A key result is that closed manifolds N which are both t-connected and codimension-2 PL fibrators are then codimension-(t+1) PL fibrators. Furthermore, when t>n/2 N has even richer PL fibrator properties, which will be described.

Date received: August 8, 2002