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THE EQUIVARIANT CHEEGER–MÜLLER THEOREM ON LOCALLY SYMMETRIC SPACES

Part of: Homology and homotopy of topological groups and related structures Partial differential equations on manifolds; differential operators

Published online by Cambridge University Press:  02 October 2014

Michael Lipnowski
Michael Lipnowski*
Affiliation:
Mathematics Department, Duke University, Box 90320, Durham, NC 27708-0320, USA (malipnow@math.duke.edu)
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Abstract

In this paper, we provide a concrete interpretation of equivariant Reidemeister torsion, and demonstrate that Bismut–Zhang’s equivariant Cheeger–Müller theorem simplifies considerably when applied to locally symmetric spaces. In a companion paper, this allows us to extend recent results on torsion cohomology growth and torsion cohomology comparison for arithmetic locally symmetric spaces to an equivariant setting.

Keywords

Reidemeister torsionanalytic torsionCheeger–Müller theoremequivariantlocally symmetric space

MSC classification

Primary: 57T99: None of the above, but in this section
Secondary: 58J52: Determinants and determinant bundles, analytic torsion
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 15 , Issue 1 , January 2016 , pp. 165 - 202
Copyright
© Cambridge University Press 2014 

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