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 ...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× R 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.展开更多
基金supported in part by Projeto Tematico Topologia Algebrica Geometrica e Differencial2008/57607-6supported in part by NSFC(Grant No.10931005)project of Beijing Municipal Education Commission(Grant No.KZ201310028030)
文摘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× R 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.
