On the growth of the first Betti number of arithmetic hyperbolic 3-manifolds
Joachim Schwermer
Universität Wien, AustriaSteffen 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