Higher Whitehead torsion and the geometric assembly map

TL;DR

This paper develops a higher Whitehead torsion map using algebraic K-theory, establishing its properties and applying it to describe a geometric assembly map in homotopy theory.

Contribution

It introduces a higher Whitehead torsion map based on algebraic K-theory and relates it to a geometric assembly map in a homotopy-theoretic framework.

Findings

Constructed a higher Whitehead torsion map with classical properties.

Connected the torsion map to a geometric assembly map.

Provided a homotopy-theoretic description of the 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.