Geodesic
On the growth of the first Betti number of arithmetic hyperbolic 3-manifolds
Steffen Kionke1 orcid ; Joachim Schwermer2
1Heinrich Heine Universität Düsseldorf, Düsseldorf, Germany
2Universität Wien, Austria
Groups, geometry, and dynamics, Tome 9 (2015) no. 2, pp. 531-565

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DOI

We give a lower bound for the first Betti number of a class of arithmetically defined hyperbolic 3-manifolds and we deduce the following theorem. Given an arithmetically defined cocompact subgroup Γ⊂SL2​(C), provided the underlying quaternion algebra meets some conditions, there is a decreasing sequence {Γi​}i​ of finite index congruence subgroups of Γ such that the first Betti number satisfies
DOI : 10.4171/ggd/320
Classification : 11-XX, 22-XX, 57-XX
Mots-clés : Arithmetic groups, cohomology, hyperbolic manifolds, Betti numbers

Steffen Kionke  1   ; Joachim Schwermer  2

1 Heinrich Heine Universität Düsseldorf, Düsseldorf, Germany
2 Universität Wien, Austria 
Steffen Kionke; Joachim Schwermer. On the growth of the first Betti number of arithmetic hyperbolic 3-manifolds. Groups, geometry, and dynamics, Tome 9 (2015) no. 2, pp. 531-565. doi: 10.4171/ggd/320
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