Let f: M → M be a homotopically periodic (that is, fk ≃ id, for some k ⩾ 1) self‐map of an infranilmanifold M. Then the Lefschetz number L(f) and the Nielsen number N(f) of the map f are the same. In particular, L(f) = N(f) for f an isometry. On the other hand, contrary to the Anosov result for nilmanifolds, |L(f)| ≃ N(f) even for f an affine Anosov diffeomorphism. However, the deviation from the equality |L(f)| = N(f) can be measured by the holonomy group of M.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.