Nielsen equalizer theory

Details Nielsen equalizer theory Nielsen equalizer theory

2010-08-12

arxiv.org/abs/1008.2154v2

Topology and its Applications 158, 2011, p. 1615-1625

Mathematics

General Topology

+ addendum, sync with published version

Scientific paper

10.1016/j.topol.2011.05.032

We extend the Nielsen theory of coincidence sets to equalizer sets, the points where a given set of (more than 2) mappings agree. On manifolds, this theory is interesting only for maps between spaces of different dimension, and our results hold for sets of k maps on compact manifolds from dimension (k-1)n to dimension n. We define the Nielsen equalizer number, which is a lower bound for the minimal number of equalizer points when the maps are changed by homotopies, and is in fact equal to this minimal number when the domain manifold is not a surface. As an application we give some results in Nielsen coincidence theory with positive codimension. This includes a complete computation of the geometric Nielsen number for maps between tori.

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