Topological Equivalence of Linear Representations for Cyclic Groups, I & II

Abstract

In the two parts of this paper we solve a problem of De Rham, proving that Reidemeister torsion invariants determine topological equivalence of linear G-representations, for G a finite cyclic group. Methods in controlled K-theory and surgery theory are developed to establish, and effectively calculate, a necessary and sufficient condition for non-linear similarity in terms of the vanishing of certain non-compact transfer maps. For cyclic groups of 2-power order, we obtain a complete classification of non-linear similarities.

The first version of this paper appeared as MPI Preprint 1997-58, Max Planck Institut fuer Mathematik, Bonn. The final version includes many improvements in exposition and new results. It is now divided into two parts. Part I (36 pages) will appear in Annals of Mathematics, and Part II (43 pages) will appear in Forum Math