Torsion of digraphs and path complexes
Alexander Asaturovich Grigor'yan, Yong Lin, Shing–Tung Yau · arXiv (Cornell University) · 2020
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.