Higher Whitehead torsion and the geometric assembly map

Abstract

We construct a higher Whitehead torsion map, using algebraic K-theory of spaces, and show that it satisfies the usual properties of the classical Whitehead torsion. This is used to describe a "geometric assembly map" defined on stabilized structure spaces in purely homotopy theoretic terms.

46 pages. Revised version following the referee's suggestions. To appear in Journal of Topology