Nielsen coincidence theory for $(n,m)$-valued pairs

Karel Dekimpe; Lore De Weerdt

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arXiv · 2610.29274

Nielsen coincidence theory for $(n,m)$-valued pairs

Karel Dekimpe·Lore De Weerdt

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Abstract

We define a Nielsen coincidence number for pairs of maps $(f,g)$ where $f$ is $n$-valued and $g$ is $m$-valued. The classical definition of the Nielsen number does not work in this setting, but we propose a theory where coincidence classes are allowed to overlap. We invoke a notion of multiplicity of a coincidence point, which indicates to how many classes it can belong, and we show that our Nielsen number is a homotopy-invariant lower bound for the number of coincidence points with multiplicity. We show a computational result in terms of single-valued lift factors, and using this, a Wecken property for self-maps of the circle.

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BibTeX RIS

Karel Dekimpe, Lore De Weerdt. 2026-10-21. Nielsen coincidence theory for $(n,m)$-valued pairs. https://arxiv.org/abs/2610.29274

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