Nielsen numbers and Lefschetz numbers on solvmanifolds

Abstract

A compact solvmanifold S is a homogeneous space of a simply connected solvable Lie group: S = S/H, with H C S a uniform subgroup. If /: S - S is a continuous self map on S, we show that \L(f)\ < N(f), where N(f) is the Nielsen number of / and L(f) is the Lefschetz number of /. Necessary conditions and sufficient conditions in terms of \{S) and /# are found for the equality N(f) = \L(f)\ to hold.