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 $X$.

References in corpus (2)

• An averaging formula for Nielsen numbers of affine n-valued maps on infra-nilmanifolds
• Non-affine $n$-valued maps on tori

Cited by in corpus (1)

• Nielsen numbers of $n$-valued maps on infra-solvmanifolds