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arXiv · 2409.17794

Averaging formulas for the Reidemeister trace, Lefschetz and Nielsen numbers of $n$-valued maps

Karel Dekimpe·Lore De Weerdt
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Abstract

For an $n$-valued self-map $f$ of a closed manifold $X$, we prove an averaging formula for the Reidemeister trace of $f$ in terms of the Reidemeister coincidence traces of single-valued maps between finite orientable covering spaces of $X$. We then derive analogous formulas for the Lefschetz and Nielsen numbers of $f$. In the special case where $X$ is an infra-nilmanifold, we obtain explicit formulas for the Lefschetz and Nielsen numbers of any $n$-valued map on $X$.

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Karel Dekimpe, Lore De Weerdt. 2024-09-26. Averaging formulas for the Reidemeister trace, Lefschetz and Nielsen numbers of $n$-valued maps. https://doi.org/10.1007/s11784-025-01194-3

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