Coincidence theory for infra-nilmanifolds

D. Anosov shows that N(f)=|L(f)| for all continuous selfmaps f on a nilmanifold. For a given selfmap f on an infra-nilmanifold, K.B. Lee provides a criterion to determine whether N(f)=|L(f)|. Using this criterion, D. Anosov's theorem has been generalised to different classes of infra-nilmanifolds. In this article, we generalise K.B. Lee's criterion to coincidence theory. Additionally, we generalise the coincidence counterpart of D. Anosov's theorem to a well-described class of infra-nilmanifolds with cyclic holonomy group. We also give various examples illustrating that not all of the above-mentioned generalisations of D. Anosov's theorem have a counterpart in coincidence theory.