Lefschetz and Nielsen coincidence numbers on nilmanifolds and solvmanifolds, II

AbstractMcCord (1991) claimed that Nielsen coincidence numbers and Lefschetz coincidence numbers are related by the inequality N(f, g) ⩾ ¦L(f, g)¦ for all maps f,g:S1 → S2 between compact orientable solvmanifolds of the same dimension. It was further claimed that N(f, g) = ¦L(f, g)¦ when S2 is a nilmanifold. A mistake in that paper has been discovered. In this paper, that mistake is partially repaired. A new proof of the equality N(f, g) = ¦L(f, g)¦ for nilmanifolds is given, and a variety of conditions for maps on orientable solvmanifolds are established which imply the inequality N(f, g) ⩾ ¦L(f, g)¦. However, it still remains open whether N(f,g) ⩾ ¦L(f,g)¦ for all maps between orientable solvmanifolds