On the gluing formula for the analytic torsion
type: Item
instance of: scholarly article
title: On the gluing formula for the analytic torsion
zbMATH Open document ID: 1318.58018
author: Jochen Brüning
author: Xiaonan Ma
published in: Mathematische Zeitschrift
publication date: 2013-03-28T00:00:00Z
review text: 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)].
reviewed by: Magnus Goffeng
Mathematics Subject Classification ID: 58J52
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 6149055
zbMATH Keywords: gluing formula
zbMATH Keywords: analytic torsion
MaRDI profile type: Publication
full work available at URL: s00209-012-1045-5
OpenAlex ID: W2161140345
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DOI: 10.1007/S00209-012-1045-5
description: scientific article; zbMATH DE number 6149055