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 \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.

References in corpus (1)

• Homologies of path complexes and digraphs

Cited by in corpus (6)

• Weighted Analytic Torsion for Weighted Digraphs
• Weighted Simplicial Complexes and Weighted Analytic Torsions
• Witten-Morse functions and Morse inequalities on digraphs
• Simplicial-like Identities for The Paths and The Regular Paths on Discrete Sets
• Discrete Differential Calculus on Simplicial Complexes and Constrained Homology
• Differential algebras on digraphs and parametrized homology