Nielsen numbers of n-valued maps on infra-solvmanifolds

2025/06/16 by Dekimpe, Karel, De Weerdt, Lore
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.13438

Abstract

We derive a formula for the Nielsen number N(f) for every n-valued self-map f of an infra-solvmanifold. To do this, we express N(f) in terms of Nielsen coincidence numbers of single-valued maps on solvmanifolds, and derive a formula for Nielsen coincidence numbers in that setting.

Citations

• Averaging formulas for the Reidemeister trace, Lefschetz and Nielsen numbers of n-valued maps
• An averaging formula for Nielsen numbers of affine n-valued maps on infra-nilmanifolds
• Nielsen numbers of affine n-valued maps on nilmanifolds
• An Averaging Formula for Nielsen numbers on Infra-Solvmanifolds
• Lifting classes for the fixed point theory of n-valued maps
• Nielsen zeta functions for maps on infra-nilmanifolds are rational

Related

• An Averaging Formula for Nielsen numbers on Infra-Solvmanifolds
• An averaging formula for Nielsen numbers of affine n-valued maps on infra-nilmanifolds
• The Nielsen numbers of iterations of maps on infra-solvmanifolds of type R and periodic points
• The Nielsen and the Reidemeister numbers of maps on infra-solvmanifolds of type (R)
• On the rationality of the Nielsen zeta function for maps on solvmanifolds