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：multivalued maps fixed points Wecken property Nielsen numbers braids configuration space 

摘      要：Abstract In this paper, we explore the fixed point theory of n-vaiued 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 S2） has the Wecken property for n-valued maps for all n ∈N （resp. all n ≥ 3）. In the case n = 2 and S2, we prove a partial result about the Wecken property. We then describe the Nielsen number of a non-split n-valued map φ ： X → X of an orientable, compact manifold without boundary in terms of the Nielsen coincidence numbers of a certain finite covering q： ）→ X with a subset of the coordinate maps of a lift of the n-valued split map → q ： →X.