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arXiv · 1305.1650

Nielsen coincidence theory of fibre-preserving maps and Dold's fixed point index

Daciberg L. Gonçalves·Ulrich Koschorke
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Abstract

Let M to B, N to B be fibrations and f1,f2 :M to N be a pair of fibre-preserving maps. Using normal bordism techniques we define an invariant which is an obstruction to deforming the pair f1,f2 over B to a coincidence free pair of maps.In the special case where the two fibrations are the same and one of the maps is the identity, a weak version of our {\omega}-invariant turns out to equal Dold's fixed point index of fibre-preserving maps. The concepts of Reidemeister classes and Nielsen coincidence classes over B are developed. As an illustration we compute e.g. the minimal number of coincidence components for all homotopy classes of maps between S^1-bundles over S^1 as well as their Nielsen and Reidemeister numbers.

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Daciberg L. Gonçalves, Ulrich Koschorke. 2013-05-07. Nielsen coincidence theory of fibre-preserving maps and Dold's fixed point index. https://arxiv.org/abs/1305.1650

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