Averaging Formula for Nielsen Numbers

Abstract

We prove that the averaging formula for Nielsen numbers holds for continuous maps on infra-nilmanifolds: Let M be an infra-nilmanifold and ƒ : M → M be a continuous map. Suppose M K is a regular covering of M which is a compact nilmanifold with π 1 (M K = K . Assume that f * (K) ⊂ K . Then ƒ has a lifting . We prove a question raised by McCord, which is for any with an essential fixed point class, fix =1. As a consequence, we obtain the following averaging formula for Nielsen numbers