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

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 $X$.

Theorems & Definitions (33)

• Remark 2.1
• Theorem 2.2: leestaecker
• Remark 2.3
• Remark 2.4
• Theorem 2.5: staecker2023
• Example 2.6
• Definition 3.1
• Remark 3.2
• Lemma 3.3
• proof