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arXiv · 1103.2262

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

Simon Marshall·Werner Mueller
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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 Mueller. 2011-03-11. On the torsion in the cohomology of arithmetic hyperbolic 3-manifolds. https://doi.org/10.1215/00127094-2080850

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