Speaker
F. Thomas Farrell
(YMSC and Dept. of Mathematics Tsinghua University)
Description
This talk is a report on joint work with W. Lueck and W. Steimle. Let $p:M \to B$ be a continuous map between closed connected manifolds such the induced map $P$ on fundamental groups is an epimorphism and $B$ is aspherical. Let $F(p)$ denote the homotopy fiber of $p$. An explicit model for $F(p)$ is the covering space of $M$ corresponding to the kernel of $P$.) The question addressed in this talk is to give useful sufficient conditions which guarantee that $p$ is homotopic to an approximate manifold fibration $q:M \to B$; i.e. a continuous map such that $q^{-1}(U)$ is homotopy equivalent to $F(p)$ for each open subset $U$ of $B$ which is homeomorphic to $R^n$ where $n= \dim B$. We do this for a large class of aspherical manifolds $B$ including all negatively curved manifolds of dimension different from 4.
