Analytic and Reidemeister Torsions of Digraphs and Path Complexes

Explore the concepts of Reidemeister and analytic torsions on finite digraphs through the lens of path homology theory in this 43-minute lecture. Delve into the construction of a preferred basis for the path complex on a digraph G using homology basis, leading to the definition of Reidemeister torsion τ(G). Examine the Hodge Laplace operator Δp acting on p-paths and its role in defining analytic torsion T(G) on graphs. Discover the proven identity between these two torsion notions and learn formulas for torsions of Cartesian products and joins of digraphs. This talk, presented by Yong Lin at BIMSA, is based on collaborative work with A. Grigoryan and S.T. Yau, offering insights into advanced mathematical concepts in graph theory and topology.

Yong Lin: Analytic and Reidemeister torsions of digraphs and path complexes #ICBS2024