Nielsen numbers of periodic maps on solvmanifolds

Abstract

Let f : M → M f:M \to M be a self-map of a solvmanifold M M . Then the Lefschetz number L ( f ) L(f) and the Nielsen number N ( f ) N(f) of f f satisfy | L ( f ) | ≤ N ( f ) |L(f)| \leq N(f) . If f f is homotopically periodic (i.e., f k ≃ id {f^k} \simeq {\text {id}} , for some k ≥ 1 k \geq 1 ), then L ( f ) = N ( f ) L(f) = N(f) .