Fixed points of n-valued maps on surfaces and the Wecken property a configuration space approach

作     者：GONCALVES Daciberg Lima GUASCHI John 

作者机构：Departamento de Matemdtica&IMEUniversidade de Sao PauloSdo Paulo 05508-090Brazil Laboratoire de Mathematiques Nicolas Oresme UMR CNRS 6139UNICAENNormandie UniversiteCS 1403214032 Caen Cedex 5France 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2017年第60卷第9期

页      面：1561-1574页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by Fundao de Amparo a Pesquisa do Estado de So Paulo(FAPESP) Projeto Temtico Topologia Algébrica,Geométrica e Diferencial(Grant No.2012/24454-8) supported by the same project as well as the Centre National de la Recherche Scientifique(CNRS)/Fundao de Amparo a Pesquisa do Estado de So Paulo(FAPESP)Projet de Recherche Conjoint(PRC)project(Grant No.275209) 

主　　题：配置空间 地图 n值 Nielsen数 性质 固定点 曲面 不动点理论 

摘      要：In this paper, we explore the fixed point theory of n-valued maps using configuration spaces and braid groups, focusing on two fundamental problems, the Wecken property, and the computation of the Nielsen number. We show that the projective plane(resp. the 2-sphere S^2) has the Wecken property for n-valued maps for all n ∈ N(resp. all n 3). In the case n = 2 and S^2, we prove a partial result about the Wecken *** then describe the Nielsen number of a non-split n-valued map ? : X■X of an orientable, compact manifold without boundary in terms of the Nielsen coincidence numbers of a certain finite covering q : X → X with a subset of the coordinate maps of a lift of the n-valued split map ? ? q : X■X.