Torsion of digraphs and path complexes
Combinatorics
2020-12-15 v1 Algebraic Topology
Abstract
We define the notions of Reidemeister torsion and analytic torsion for directed graphs by means of the path homology theory introduced by the authors in \cite{Grigoryan-Lin-Muranov-Yau2013, Grigoryan-Lin-Muranov-Yau2014, Grigoryan-Lin-Muranov-Yau2015, Grigoryan-Lin-Muranov-Yau2020}. We prove the identity of the two notions of torsions as well as obtain formulas for torsions of Cartesian products and joins of digraphs.
Cite
@article{arxiv.2012.07302,
title = {Torsion of digraphs and path complexes},
author = {Alexander Grigor'yan and Yong Lin and Shing-Tung Yau},
journal= {arXiv preprint arXiv:2012.07302},
year = {2020}
}