Approximately fibering a manifold over an aspherical one

In this talk we address the problem whether a given map from some closed connected'
manifold to an aspherical closed manifold ''approximately fibers'', i.e., is homotopic to
Manifold Approximate Fibration.
We define elements in certain algebraic K-groups which are zero if the approximate fibering
problem can be solved; under certain conditions their vanishing is also a sufficient condition.
This is joint work with Tom Farrell and Wolfgang Lück.