  We extend the Nielsen theory of coincidence sets to equalizer sets, the
points where a given set of (more than 2) mappings agree. On manifolds, this
theory is interesting only for maps between spaces of different dimension, and
our results hold for sets of k maps on compact manifolds from dimension (k-1)n
to dimension n. We define the Nielsen equalizer number, which is a lower bound
for the minimal number of equalizer points when the maps are changed by
homotopies, and is in fact equal to this minimal number when the domain
manifold is not a surface.
  As an application we give some results in Nielsen coincidence theory with
positive codimension. This includes a complete computation of the geometric
Nielsen number for maps between tori.
