Coincidence Wecken Property for Nilmanifolds

作     者：Daciberg GON?ALVES Peter WONG 

作者机构：Departamento de Matemática-IME-Universidade de S?o Paulo Rua do Mat?o Department of Mathematics Bates College 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2019年第35卷第2期

页      面：239-244页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported in part by Projeto Temático Topologia Algébrica Geométrica e Differencial(Grant No.2016/24707-4) 

主　　题：Nielsen coincidence theory nilmanifolds 

摘      要：Let f, g: X → Y be maps from a compact infra-nilmanifold X to a compact nilmanifold Y with dim X ≥ dim Y. In this note, we show that a certain Wecken type property holds, i.e., if the Nielsen number N(f, g) vanishes then f and g are deformable to be coincidence free. We also show that if X is a connected finite complex X and the Reidemeister coincidence number R(f, g) = ∞ then f ～ f so that C(f , g) = {x ∈ X | f (x) = g(x)} is empty.