The set of self-mapping degrees of S^3-geometry 3-manifolds in[2]have some mistakes when the fundamental group of the 3-manifold is D4n^*,O48^*,D'n·2q or T'8·3q.So we need to make this errata.The sel...The set of self-mapping degrees of S^3-geometry 3-manifolds in[2]have some mistakes when the fundamental group of the 3-manifold is D4n^*,O48^*,D'n·2q or T'8·3q.So we need to make this errata.The self-mapping degrees of all closed and oriented 3-manifolds are listed in[1]and[5].The table of spherical case in[5]is mostly quoted from[2].The results in[5]which do not involve the corrections made here still valid.The results in[5]involving the corrections made here should be also changed.展开更多
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
We give a brief survey of some developments in Nielsen fixed point theory. After a look at early history and a digress to various generalizations, we confine ourselves to several topics on fixed points of self-maps on...We give a brief survey of some developments in Nielsen fixed point theory. After a look at early history and a digress to various generalizations, we confine ourselves to several topics on fixed points of self-maps on manifolds and polyhedra. Special attention is paid to connections with geometric group theory and dynamics, as well as some formal approaches.展开更多
基金Supported by NSFC(Grant Nos.11571246,11431009,11661131004)the Fundamental Research Funds for the Central Universities in China
文摘The set of self-mapping degrees of S^3-geometry 3-manifolds in[2]have some mistakes when the fundamental group of the 3-manifold is D4n^*,O48^*,D'n·2q or T'8·3q.So we need to make this errata.The self-mapping degrees of all closed and oriented 3-manifolds are listed in[1]and[5].The table of spherical case in[5]is mostly quoted from[2].The results in[5]which do not involve the corrections made here still valid.The results in[5]involving the corrections made here should be also changed.
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.
基金Supported by NSF of China(Grant Nos.11131008,11431009)
文摘We give a brief survey of some developments in Nielsen fixed point theory. After a look at early history and a digress to various generalizations, we confine ourselves to several topics on fixed points of self-maps on manifolds and polyhedra. Special attention is paid to connections with geometric group theory and dynamics, as well as some formal approaches.
