The Metric Anomaly of Analytic Torsion at the Boundary of an Even Dimensional Cone

Details The Metric Anomaly of Analytic Torsion at the Boundary of an Even Dimensional Cone The Metric Anomaly of Analytic Torsion at the Boundary of an Even Dimensional Cone

2010-04-12

arxiv.org/abs/1004.2069v2

Mathematics

Spectral Theory

33 pages, 2 figures, completely revised. Published in Annals of Global Analysis and Geometry

Scientific paper

The formula for analytic torsion of a cone in even dimensions is comprised of three terms. The first two terms are well understood and given by an algebraic combination of the Betti numbers and the analytic torsion of the cone base. The third "singular" contribution is an intricate spectral invariant of the cone base. We identify the third term as the metric anomaly of the analytic torsion coming from the non-product structure of the cone at its regular boundary. Hereby we filter out the actual contribution of the conical singularity and identify the analytic torsion of an even-dimensional cone purely in terms of the Betti numbers and the analytic torsion of the cone base.

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