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 ...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.展开更多
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).
文摘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.
基金Wang is funded by Science and Technology Project of Hebei Education Department(No.ZD2022168)Project of Cangzhou Normal University(No.XNJJLYB2021006)+3 种基金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)。
基金supported by Scientific Research Project of Hebei Education Department(No.QN2019333)Natural Fund Project of Cangzhou Science and Technology Bureau(No.197000002)+2 种基金Project of Cangzhou Normal University(No.xnjjl1902)supported by Postdoctoral International Exchange Program of China 2019 and NSFC(No.12001310)supported by NSFC(No.11671401)。
基金Supported by the Science and Technology Project of Hebei Education Department(QN2019333)the Natural Fund of Cangzhou Science and Technology Bureau(197000002)+1 种基金Project of Cangzhou Normal University(xnjjl1902)NSFC(12001310)。
