Lefschetz and Nielsen coincidence numbers on nilmanifolds and solvmanifolds

AbstractSuppose M1,M2 are compact, connected orientable manifolds of the same dimension. Then for all pairs of maps ƒ,g:M1→M2, the Nielsen coincidence number N(ƒ,g) and the Lefschetz coincidence number L(ƒ,g) are measures of the number of coincidences of ƒ and g: points x∈M1 with f(x)=g(x). A manifold is a nilmanifold (solvmanifold) if it is a homogenous space of a nilpotent (solvable) Lie group. If M1 and M2 are compact connected orientable solvmanifolds, then N(ƒ, g)⩾|L(ƒ, g)| for all ƒ and g, with equality for all ƒ and g if M2 is a nilmanifold