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

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

2011-03-11

arxiv.org/abs/1103.2262v1

Mathematics

Number Theory

22 pages

Scientific paper

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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