Duke Mathematical Journal

On the torsion in the cohomology of arithmetic hyperbolic 3-manifolds

Simon Marshall and Werner Müller

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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.

Article information

Duke Math. J., Volume 162, Number 5 (2013), 863-888.

First available in Project Euclid: 29 March 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F75: Cohomology of arithmetic groups
Secondary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]


Marshall, Simon; Müller, Werner. On the torsion in the cohomology of arithmetic hyperbolic 3-manifolds. Duke Math. J. 162 (2013), no. 5, 863--888. doi:10.1215/00127094-2080850. https://projecteuclid.org/euclid.dmj/1364562913

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