Weak Graph Map Homotopy and Its Applications  

作　　者：Conglei ZHANG Yanying WANG Zhiguo ZHANG Yan ZHAO 

机构地区：[1]School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China [2]Department of Basic Science,Shanxi Agricultural University,Jinzhang 030801,Shanxi,China [3]Center for Topology and Geometry based Technology,School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China [4]School of Mathematical Sciences,Hebei Normal University,Taiyuan 030031,China [5]School of Mathematics and Computer Science,Shanxi Normal University,Shijiazhuang 050024,China [6]School of Mathematics and Science,Hebei GEO University,Shijiazhuang 050031,China

出　　处：《Chinese Annals of Mathematics,Series B》2024年第2期235-252,共18页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11771116)。

摘　　要：The authors introduce a notion of a weak graph map homotopy(they call it M-homotopy),discuss its properties and applications.They prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in 2001.The difference between them is that the weak graph map homotopy transformation is defined in terms of maps,while the graph homotopy transformation is defined by means of combinatorial operations.They discuss its advantages over the graph homotopy transformation.As its applications,they investigate the mapping class group of a graph and the 1-order M P-homotopy group of a pointed simple graph.Moreover,they show that the 1-order M P-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.

关 键 词：Weak graph map homotopy Trivial vertex Strong deformation retract Mapping class group MP-Homotopy group 

分 类 号：O157.5[理学—数学]