Arbeitsgemeinschaft mit aktuellem Thema: Higher Torsion Invariants in Differential Topology and Algebraic K-Theory

Abstract

The purpose of this Arbeitsgemeinschaft was to study and—as far as possible—compare three generalisations of the classical Franz-Reidemeister torsion to families E → B of manifolds. Dwyer, Weiss and Williams construct higher torsion as a byproduct of a family index theorem for the fibrewise A-theory Euler-class. Igusa and Klein use generalised fibrewise Morse functions to construct a classifying map from B to a Whitehead space, and to pull-back universal classes from there. Bismut and Lott prove an analytic family index theorem for flat vector bundles and obtain the higher analytic torsion as a transgression.