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Analytic torsion for graphs

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arxiv 2201.09412 v1 pith:FMSIVATH submitted 2022-01-24 math.CO cs.DM

Oliver Knill This is my paper · ORCID
classification math.COcs.DM
keywords analytictorsiongraphgraphsalgebracontinuumcontractiblecorresponds
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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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  1. Remarks about Connection and Dirac matrices

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    The eigenvalues of the connection and Dirac matrices of a finite simplicial complex are bounded above by the ordered connection and Dirac degrees, while the headline claim that the connection matrix dominates the Dira...

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