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

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

2001-09-05

arxiv.org/abs/math/0109036v2

Mathematics

Geometric Topology

The first version of this paper appeared as MPI Preprint 1997-58, Max Planck Institut fuer Mathematik, Bonn. The final version

Scientific paper

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.

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