Nielsen numbers and Lefschetz numbers on solvmanifolds

Christopher K. McCord

Vol. 147 (1991), No. 1, 153–164

DOI: 10.2140/pjm.1991.147.153

Abstract

A compact solvmanifold S is a homogeneous space of a simply connected solvable Lie group: S = S∕H, with H ⊆S a uniform subgroup. If f : S → S is a continuous self map on S, we show that |L(f)|≤ N(f), where N(f) is the Nielsen number of f and L(f) is the Lefschetz number of f. Necessary conditions and sufficient conditions in terms of π₁(S) and f_# are found for the equality N(f) = |L(f)| to hold.

Mathematical Subject Classification 2000

Primary: 55M20

Secondary: 53C30, 55R10, 57S99

Milestones

Received: 21 February 1989

Revised: 3 July 1989

Published: 1 January 1991