有向图的基本群和覆盖  

Fundamental Groups and Covering of Digraphs

作　　者：王冲[1] 任世全 刘秀贵[3] WANG Chong;REN Shiquan;LIU Xiugui(Department of Mathematics and Statistics,Cangzhou Normal University,Cangzhou,Hebei,061000,P.R.China;School of Mathematics and Statistics,Henan University,Kaifeng,Henan,475004,P.R.China;School of Mathematical Sciences,Nankai University,Tianjin,300071,P.R.China)

机构地区：[1]沧州师范学院数学与统计系,河北沧州061000 [2]河南大学数学与统计学院,河南开封475004 [3]南开大学数学科学学院,天津300071

出　　处：《数学进展》2023年第2期235-249,共15页Advances in Mathematics（China）

基　　金：Wang is funded by Science and Technology Project of Hebei Education Department(No.ZD2022168);Project of Cangzhou Normal University(No.XNJJLYB2021006);Ren is supported by NSFC(No.12001310);Liu is supported in part by NSFC(No.12171165);China Postdoctoral Science Foundation(No.2020M680494);Tianjin Natural Science Foundation(No.19JCYBJC30200)。

摘　　要：本文基于范畴理论,主要研究了有向图和其对应的无向图(简称为图)在不同同伦等价意义下基本群之间的关系,证明了覆盖映射所诱导的覆盖图和底图的基本群之间的同态是单同态.设G是连通有向图,G是G的万有覆盖,覆盖映射为p.我们证明了G的覆盖转化群D(G,p)同构于G在C-同伦意义下的基本群.In this paper,based on the functors between digraphs and graphs,we study the relations among their fundamental groups under different homotopy equivalence,and prove that the homomorphisms between fundamental groups induced by covering mappings are monomorphisms.Let G be a connected digraph and G be the universal cover of G with covering map p.We prove that the group D(G,p)of covering translations of G is isomorphic to the fundamental group of G formed by equivalence classes of based loops under C-homotopy.

关 键 词：C-同伦 基本群 覆盖有向图 同伦提升性质 

分 类 号：O189.23[理学—数学]