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. Anosovʹs theorem has been generalised to different classes of infra-nilmanifolds. In this article, we generalise K.B. Leeʹs criterion to coincidence theory. Additionally, we generalise the coincidence counterpart of D. Anosovʹs 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. Anosovʹs theorem have a counterpart in coincidence theory.