Analytic torsion is a concept in mathematical analysis, particularly in the fields of differential geometry and topology, relating to the behavior of certain types of Riemannian manifolds. It arises in the context of studying the spectral properties of differential operators, especially the Laplace operator.
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Analytic torsion is a spectral invariant constructed from regularized determinants of the Laplacians on differential forms with suitable flat coefficients. It is the analytic counterpart of combinatorial Reidemeister torsion, whose refinements include Turaev torsion; equality theorems relate the spectral and combinatorial invariants under appropriate hypotheses on the manifold and coefficients.