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

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

Let M be a compact 3-manifold with infinite fundamental group . Given a homomorphism from to a p-adic analytic group G with dense image, we describe the possible mod-p homology growth of covers Mn of M determined by the congruence subgroups Gn. If d D dim.G/ > 3, this growth is always non-trivial, growing at least as fast as Vol.Mn/ 1/=d . Mathematics Subject Classification (2010). 22E40.

M. Emerton | Frank Calegari

[1] M. Emerton,et al. Non-abelian Fundamental Groups and Iwasawa Theory: Completed cohomology – a survey , 2011 .

[2] Simon Marshall. Bounds for multiplicities of automorphic forms of cohomological type on GL_2 , 2010, 1002.3569.

[3] Marc Lackenby,et al. Large groups, property (τ) and the homology growth of subgroups , 2009, Mathematical Proceedings of the Cambridge Philosophical Society.

[4] M. Emerton,et al. Bounds for multiplicities of unitary representations of cohomological type in spaces of cusp forms , 2007, 0704.0662.

[5] M. Lackenby. Detecting large groups , 2007, math/0702571.

[6] N. Boston,et al. Pro–$p$ groups and towers of rational homology spheres , 2006, 0902.4567.

[7] K. Brown,et al. Ring-Theoretic Properties of Iwasawa Algebras: A Survey 1 , 2005, math/0511345.

[8] N. Dunfield,et al. Automorphic forms and rational homology 3--spheres , 2005, math/0508271.

[9] D. Rolfsen. Knots and Links , 2003 .

[10] O. Venjakob. On the structure theory of the Iwasawa algebra of a p-adic Lie group , 2001, math/0106269.

[11] J. Dixon,et al. Analytic Pro-P Groups , 1999 .

[12] A. Lubotzky. Group presentation, $p$-adic analytic groups and lattices in $\mathrm{SL}_2(\mathbf{C})$ , 1983 .

[13] M. Lazard,et al. Groupes analytiques p-adiques , 1965 .

[14] W. J. Barnes. Group at presentation , .