THE ANOSOV THEOREM FOR INFRA-NILMANIFOLDS WITH A2-PERFECT HOLONOMY GROUP

摘要

In this paper, we show that N(f) = |L(f)| for any continuous selfmap f : M→4 M on an infra-nilmanifold M of which the holonomy group is 2-perfect (i.e. having no index two subgroup). Conversely, for any finite group F that is not 2-perfect, we show there exists at least one infra-nilmanifold M with holonomy group F and a continuous selfmap f M→M such that N(f)≠|L(f)|.