LEFSCHETZ AND NIELSEN COINCIDENCE NUMBERS ON NILMANIFOLDS AND SOLVMANIFOLDS

Suppose M1, M2 are compact, connected orientable manifolds of the same dimension. Then for all pairs of maps f, g:M1 --> M2, the Nielsen coincidence number N(f, g) and the Lefschetz coincidence number L(f, g) are measures of the number of coincidences of f and g: points x is-an-element-of M1 with f(x) = g(x). A manifold is a nilmanifold (solvmanifold) if it is a homogeneous space of a nilpotent (solvable) Lie group. If M1 and M2 are compact connected orientable solvmanifolds, then N(f, g) greater-than-or-equal-to \L(f, g)\ for all f and g, with equality for all f and g if M2 is a nilmanifold.