Anomaly formulas for the complex-valued analytic torsion on compact bordisms

Details Anomaly formulas for the complex-valued analytic torsion on compact bordisms Anomaly formulas for the complex-valued analytic torsion on compact bordisms

2012-01-23

arxiv.org/abs/1201.4753v1

Mathematics

Differential Geometry

26 pages

Scientific paper

We extend the analytic Burghelea--Haller torsion to compact Riemannian bordisms, by studying non-selfadjoint Laplacians and considering absolute and relative boundary conditions. In this context, we obtain anomaly formulas for the analytic Burghelea--Haller torsion based on the work by Bruening and Ma for the Ray--Singer metric on maniflods with boundary. In odd dimensions, our anomaly formulas are in accord with the corresponding results of Su, without requiring the variations of the Riemannian metric and bilinear structures to be supported in the interior of the manifold. Our results are proved by using invariance theory for the coefficients of the heat kernel asymptotic expansion and an argument of analytic continuation.

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