The asymptotic growth of torsion homology for arithmetic groups

By Nicolas Bergeron, Akshay Venkatesh. Journal of the Institute of Mathematics of Jussieu, 2010

193 citations recorded by the source corpus.

Abstract When does the amount of torsion in the homology of an arithmetic group grow exponentially with the covolume? We give many examples where this is the case, and conjecture precise conditions.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f9afca7a1b1f0ab1e2be06b81a15c80785a253ec

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Citations in the corpus

3-Manifold Groups (2012, background): “olic 3-manifolds. Arguably the most interesting question is about the growth rate of the size of in the homology of ﬁnite covers. The following question has been raised by several authors (see, e.g., [BV13], [Lu¨02, Question 13.73] and [Lu¨12, Conjecture 1.12]). Question 9.12. Let Nbe an irreducible”
On the growth of $L^2$-invariants for sequences of lattices in Lie groups (2012, methodology): “We will work in the setting of [24]: here we will be as brief as possible concerning definitions, etc.”
A torsion Jacquet--Langlands correspondence (2012, background): “For such groups, it has been observed (both numerically and theoretically) that H1(Γ,Z) = Γab has a large torsion subgroup [6, 72].”
Torsion homology growth and cycle complexity of arithmetic manifolds (2014, background): “at (2.6.1) logTan(Mi) Vi →τ(2) H3 =− 1 6π . It follows from the deﬁnition of analytic torsion and well known properties of the spectrum of the Laplace operators on Riemannian 3-manifolds (see e.g. in [7]) that it is enough toprovethat (2.6.2) d ds ¯ ¯ s=0 1 Γ(s) Z +∞ 0 ts−1 1 Vi Z Mi tre−t∆ (2) (x˜”
p-ADIC GEOMETRY (2017, background): “gy and Galois representations extends to the full integral cohomology groups Hi(X K;Z), including their torsion subgroups, which can be enormous, especially in the case of hyperbolic 3-manifolds, cf. [BV13]. Theorem 5.1 ([Sch15]). Assume that G= Res F=Q GL n for some totally real or CM eld F. Consid”
On torsion in the cohomology of locally symmetric varieties (2013, unknown): “[12], [50].”