Let be a compact 3-manifold with infinite fundamental group . Given a homomorphism from to a -adic analytic group with dense image, we describe the possible mod- homology growth of covers of determined by the congruence subgroups . If = dim() > 3, this growth is always non-trivial, growing at least as fast as Vol().
Cite this article
Frank Calegari, Matthew Emerton, Mod- cohomology growth in -adic analytic towers of 3-manifolds. Groups Geom. Dyn. 5 (2011), no. 2, pp. 355–366