The metric anomaly of analytic torsion at the boundary of an even dimensional cone
The formula for analytic torsion of a cone in even dimensions involves three terms. The first two terms are well understood and are given by an algebraic combination of the Betti numbers and the analytic torsion of the base of the cone. The third ``singular'' contribution is an intricate spectral invariant of the cone base. The author identifies the third term as the metric anomaly of the analytic torsion coming from the non-product structure of the cone at its regular boundary. The author filters out the contribution of the conical singularity and identifies 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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