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1 April 2013 On the torsion in the cohomology of arithmetic hyperbolic 3-manifolds
Simon Marshall, Werner Müller
Duke Math. J. 162(5): 863-888 (1 April 2013). DOI: 10.1215/00127094-2080850

Abstract

In this paper we consider the cohomology of a closed arithmetic hyperbolic 3-manifold with coefficients in the local system defined by the even symmetric powers of the standard representation of SL(2,C). The cohomology is defined over the integers and is a finite abelian group. We show that the order of the 2nd cohomology grows exponentially as the local system grows. We also consider the twisted Ruelle zeta function of a closed arithmetic hyperbolic 3-manifold, and we express the leading coefficient of its Laurent expansion at the origin in terms of the orders of the torsion subgroups of the cohomology.

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Simon Marshall. Werner Müller. "On the torsion in the cohomology of arithmetic hyperbolic 3-manifolds." Duke Math. J. 162 (5) 863 - 888, 1 April 2013. https://doi.org/10.1215/00127094-2080850

Information

Published: 1 April 2013
First available in Project Euclid: 29 March 2013

zbMATH: 1316.11042
MathSciNet: MR3047468
Digital Object Identifier: 10.1215/00127094-2080850

Subjects:
Primary: 11F75
Secondary: 22E40

Rights: Copyright © 2013 Duke University Press

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Vol.162 • No. 5 • 1 April 2013
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