Smooth realizations of relative Nielsen numbers

It is known that the relative Nielsen number N(f; X, A), the Nielsen number of the complement N(f; X − A) and the Nielsen number of the closure N(f; X − A) are optimal lower bounds for the number of fixed points on X, X − A and X − A for self-maps of pairs of compact polyhedra (X, A) which satisfy fairly general assumptions. We show here that this is still true in the smooth category, i.e., that under equivalent assumptions these Nielsen type numbers are optimal lower bounds for the number of fixed points of smooth self-maps on pairs of smooth manifolds.