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Analytic torsion for graphs

Published 24 Jan 2022 in math.CO and cs.DM | (2201.09412v1)

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.

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