On the growth of the first Betti number of arithmetic hyperbolic 3-manifolds

  • Joachim Schwermer

    Universität Wien, Austria
  • Steffen Kionke

    Heinrich Heine Universität Düsseldorf, Düsseldorf, Germany

Abstract

We give a lower bound for the first Betti number of a class of arithmetically defined hyperbolic -manifolds and we deduce the following theorem. Given an arithmetically defined cocompact subgroup , provided the underlying quaternion algebra meets some conditions, there is a decreasing sequence of finite index congruence subgroups of such that the first Betti number satisfies

as goes to infinity.

Cite this article

Joachim Schwermer, Steffen Kionke, On the growth of the first Betti number of arithmetic hyperbolic 3-manifolds. Groups Geom. Dyn. 9 (2015), no. 2, pp. 531–565

DOI 10.4171/GGD/320