Coincidence Wecken Property for Nilmanifolds

Abstract

Let \(f,g : X \rightarrow Y\) be maps from a compact infra-nilmanifold X to a compact nilmanifold Y with \(X \geq \rm{dim}\it{Y}\). In this note, we show that a certain Wecken type property holds, i.e., if the Nielsen number N(f, g) vanishes then f and g are deformable to be coincidence free. We also show that if X is a connected finite complex X and the Reidemeister coincidence number R(f, g) = ∞ then f ~ f′ so that \(C(f',g)= \{x \in X|f'(x)=g(x)\}\) is empty.