数学季刊 ›› 2023, Vol. 38 ›› Issue (1): 30-49.doi: 10.13371/j.cnki.chin.q.j.m.2023.01.003
收稿日期:
2023-04-11
出版日期:
2023-03-30
发布日期:
2023-03-20
通讯作者:
WANG Chong (1981-), female, native of Baoding, Hebei, associate professor of Cangzhou Normal
University, engages in topology.
E-mail:wangchong 618@163.com
作者简介:
REN Shi-quan (1987-), male, native of Jinan, Shandong, lecturer of Henan University, engages
in topology; WANG Chong (1981-), female, native of Baoding, Hebei, associate professor of Cangzhou Normal
University, engages in topology.
基金资助:
Received:
2023-04-11
Online:
2023-03-30
Published:
2023-03-20
Contact:
WANG Chong (1981-), female, native of Baoding, Hebei, associate professor of Cangzhou Normal
University, engages in topology.
E-mail:wangchong 618@163.com
About author:
REN Shi-quan (1987-), male, native of Jinan, Shandong, lecturer of Henan University, engages
in topology; WANG Chong (1981-), female, native of Baoding, Hebei, associate professor of Cangzhou Normal
University, engages in topology.
Supported by:
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.
中图分类号:
任世全, 王冲. 有向图的加权解析挠率[J]. 数学季刊, 2023, 38(1): 30-49.
REN Shi-quan, WANG Chong. Weighted Analytic Torsion for Weighted Digraphs[J]. Chinese Quarterly Journal of Mathematics, 2023, 38(1): 30-49.
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