Weighted Analytic Torsion for Weighted Digraphs
Algebraic Topology
2023-10-12 v2
Abstract
In 2020, Alexander Grigor'yan, Yong Lin and Shing-Tung Yau [4] 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 [4], we consider the notion of weighted analytic torsion for vertex-weighted digraphs. For any non-vanishing real functions and on the vertex set, we consider the vertex-weighted digraphs with the weights . We calculate the -weighted analytic torsion by examples and prove that the -weighted analytic torsion only depend on the ratio . In particular, if the weight is of the diagonal form , then the weighted analytic torsion equals to the usual (un-weighted) torsion.
Cite
@article{arxiv.2103.09552,
title = {Weighted Analytic Torsion for Weighted Digraphs},
author = {Shiquan Ren and Chong Wang},
journal= {arXiv preprint arXiv:2103.09552},
year = {2023}
}