Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.29274

Authors: Dekimpe, Karel, De Weerdt, Lore

Language: English

Topic: Fixed Point Theorems Analysis

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Fonds Wetenschappelijk Onderzoek, Vlaamse regering

Awards: Using Lie algebra methods in the study of twisted conjugacy on residually nilpotent groups, Classification, symmetries and singularities at the frontiers of algebra, analysis and geometry., G4060687250

OpenAlex ID: W7223198408

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