In this paper we continue to study (‘strong’) Nielsen coincidence
numbers (which were introduced recently for pairs of maps between
manifolds of arbitrary dimensions) and the corresponding minimum
numbers of coincidence points and pathcomponents. We explore
compatibilities with fibrations and, more specifically, with covering
maps, paying special attention to selfcoincidence questions. As a
sample application we calculate each of these numbers for all maps
from spheres to (real, complex, or quaternionic) projective
spaces. Our results turn out to be intimately related to recent work
of D Gonçalves and D Randall concerning maps which can be deformed
away from themselves but not by small deformations; in particular,
there are close connections to the Strong Kervaire Invariant One
Problem.
