Torsion of digraphs and path complexes
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 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.
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