有向图的加权解析挠率  

Weighted Analytic Torsion for Weighted Digraphs

作　　者：任世全 王冲 REN Shi-quan;WANG Chong(School of Mathematics and Statistics,Henan University,Kaifeng 475004,China;School of Mathematics and Statistics,Cangzhou Normal University,Cangzhou 061000,China)

机构地区：[1]School of Mathematics and Statistics,Henan University,Kaifeng 475004,China [2]School of Mathematics and Statistics,Cangzhou Normal University,Cangzhou 061000,China

出　　处：《Chinese Quarterly Journal of Mathematics》2023年第1期30-49,共20页数学季刊（英文版）

基　　金：REN Shi-quan is supported by China Postdoctoral Science Foundation(Grant No.2022M721023);WANG Chong is supported by Science and Technology Project of Hebei Education Department(Grant No.ZD2022168);Project of Cangzhou Normal University(Grant No.XNJJLYB2021006).

摘　　要：In 2020,Alexander Grigor'yan,Yong Lin and Shing-Tung Yau[6]introduced the Reidemeister torsion and the analytic torsion for digraphs by means of the path complex and the path homology theory.Based on the analytic torsion for digraphs introduced in[6],we consider the notion of weighted analytic torsion for vertex-weighted digraphs.For any non-vanishing real functions f and g on the vertex set,we consider the vertex-weighted digraphs with the weights(f;g).We calculate the(f;g)-weighted analytic torsion by examples and prove that the(f;g)-weighted analytic torsion only depend on the ratio f=g.In particular,if the weight is of the diagonal form(f;f),then the weighted analytic torsion equals to the usual(un-weighted)torsion.

关 键 词：Chain complex Hodge-Laplace operator Analytic torsion HOMOLOGY DIGRAPH Weighted simplicial complex 

分 类 号：O189.2[理学—数学]