Groups, Geometry, and Dynamics

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Volume 5, Issue 2, 2011, pp. 355–366
DOI: 10.4171/GGD/131

Published online: 2011-03-06

Mod-$p$ cohomology growth in $p$-adic analytic towers of 3-manifolds

Frank Calegari[1] and Matthew Emerton[2]

(1) Northwestern University, Evanston, USA
(2) Northwestern University, Evanston, USA

Let $M$ be a compact 3-manifold with infinite fundamental group $\Gamma$. Given a homomorphism from $\Gamma$ to a $p$-adic analytic group $G$ with dense image, we describe the possible mod-$p$ homology growth of covers $M_n$ of $M$ determined by the congruence subgroups $G_n$. If $d$ = dim($G$) > 3, this growth is always non-trivial, growing at least as fast as Vol($M_n$)$^{(d-1)/d}$.

Keywords: 3-manifolds, homology, lattices

Calegari Frank, Emerton Matthew: Mod-$p$ cohomology growth in $p$-adic analytic towers of 3-manifolds. Groups Geom. Dyn. 5 (2011), 355-366. doi: 10.4171/GGD/131