On the gluing formula for the analytic torsion
The objects of study in this paper are gluing formulas for analytic torsion and Cheeger-Müller/Bismut-Zhang type theorems for flat bundles on manifolds with boundary under minimal assumptions. The main technical tool is the anomaly formula of the authors [Geom. Funct. Anal. 16, No. 4, 767--837 (2006; Zbl 1111.58024)]. The anomaly formula describes the variation of analytic torsion when carrying the Riemannian metric and the metric on the flat bundle. A Cheeger-Müller/Bismut-Zhang type theorem computes the difference between the Ray-Singer metric on the determinant line of cohomology and the Reidemeister metric constructed from a Morse function. The results of the paper generalizes a result of \textit{W. Lück} [J. Differ. Geom. 37, No. 2, 263--322 (1993; Zbl 0792.53025)] proven under more restrictive assumptions: the Riemannian metric is assumed to be of product type near the boundary and the metric on the flat bundle is the flat metric. See also [the authors, ibid. 278, No. 1--2, 615--616 (2014; Zbl 1334.58021)].
scientific article; zbMATH DE number 6149055
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