Analytic torsion for graphs

2022/01/24 by Oliver Knill, Knill, Oliver · 1 voice
Computer Science · Engineering · Mathematics · #Control and Stability of Dynamical Systems #cs.DM #math.CO

paper · pdf · doi:10.48550/arxiv.2201.09412

openalex publication_date 2022/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Analytic torsion is a functional on graphs which only needs linear algebra to be defined. In the continuum it corresponds to the Ray-Singer analytic torsion. We have formulas for analytic torsion if the graph is contractible or if it is a discrete sphere. A key insight is that analytic torsion is the super determinant of the Dirac operator of the graph.

Discussions

• Analytic torsion for graphs is the new invariant in town for topological machine learning. First time I see a super determinant in my life. arxiv.org/abs/2201.09412 [bsky, 7 points, 0 comments]

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