JournalsggdVol. 5, No. 2pp. 355–366

Mod-pp cohomology growth in pp-adic analytic towers of 3-manifolds

  • Frank Calegari

    Northwestern University, Evanston, USA
  • Matthew Emerton

    Northwestern University, Evanston, USA
Mod-$p$ cohomology growth in $p$-adic analytic towers of 3-manifolds cover
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Abstract

Let MM be a compact 3-manifold with infinite fundamental group Γ\Gamma. Given a homomorphism from Γ\Gamma to a pp-adic analytic group GG with dense image, we describe the possible mod-pp homology growth of covers MnM_n of MM determined by the congruence subgroups GnG_n. If dd = dim(GG) > 3, this growth is always non-trivial, growing at least as fast as Vol(MnM_n)(d1)/d^{(d-1)/d}.

Cite this article

Frank Calegari, Matthew Emerton, Mod-pp cohomology growth in pp-adic analytic towers of 3-manifolds. Groups Geom. Dyn. 5 (2011), no. 2, pp. 355–366

DOI 10.4171/GGD/131