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A GLUING FORMULA FOR THE ANALYTIC TORSION ON HYPERBOLIC MANIFOLDS WITH CUSPS

Part of: Global differential geometry Partial differential equations on manifolds; differential operators

Published online by Cambridge University Press:  01 July 2015

Jonathan Pfaff
Jonathan Pfaff*
Affiliation:
Universität Bonn, Mathematisches Institut, Endenicher Alle 60, D-53115 Bonn, Germany (pfaff@math.uni-bonn.de)
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Abstract

For an odd-dimensional oriented hyperbolic manifold with cusps and strongly acyclic coefficient systems, we define the Reidemeister torsion of the Borel–Serre compactification of the manifold using bases of cohomology classes defined via Eisenstein series by the method of Harder. In the main result of this paper we relate this combinatorial torsion to the regularized analytic torsion. Together with results on the asymptotic behaviour of the regularized analytic torsion, established previously, this should have applications to study the growth of torsion in the cohomology of arithmetic groups. Our main result is established via a gluing formula, and here our approach is heavily inspired by a recent paper of Lesch.

Keywords

analytic torsionlocally symmetric manifoldsReidemeister torsion

MSC classification

Primary: 58J52: Determinants and determinant bundles, analytic torsion
Secondary: 53C35: Symmetric spaces
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 16 , Issue 4 , September 2017 , pp. 673 - 743
Copyright
© Cambridge University Press 2015 

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