Nielsen theory on 3-manifolds covered by S 2 . .

Let f : M . M be a self-map of a closed manifold M of dimension dim M . 3. The Nielsen number N(f) of f is equal to the minimal number of fixed points of f. among all self-maps f. in the homotopy class of f. In this paper, we determine N(f) for all self-maps f when M is a closed 3-manifold with S 2 . . geometry. The calculation of N(f) relies on the induced homomorphisms of f on the fundamental group and on the second homotopy group of M.