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

Ian Hambleton; Erik K. Pedersen

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arXiv · math/0109036

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

Ian Hambleton·Erik K. Pedersen

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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.

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BibTeX RIS

Ian Hambleton, Erik K. Pedersen. 2004-04-14. Topological Equivalence of Linear Representations for Cyclic Groups, I & II. https://arxiv.org/abs/math/0109036

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