On the non-vanishing of the first Betti number of hyperbolic three manifolds

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dc.creatorRajan, C. S.
dc.date2003-02-19
dc.date.accessioned2026-07-07T04:55:24Z
dc.date.available2026-07-07T04:55:24Z
dc.descriptionWe show the non-vanishing of cohomology groups of sufficiently small congruence lattices in $SL(1,D)$, where $D$ is a quaternion division algebras defined over a number field $E$ contained inside a solvable extension of a totally real number field. As a corollary, we obtain new examples of compact, arithmetic, hyperbolic three manifolds, with non-torsion first homology group, confirming a conjecture of Thurston. The proof uses the characterisation of the image of solvable base change by the author, and the construction of cusp forms with non-zero cusp cohomology by Labesse and Schwermer.
dc.description7 pages
dc.identifierhttps://arxiv.org/abs/math/0302226
dc.identifierhttp://arxiv.org/abs/math/0302226
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66569
dc.subjectRepresentation Theory
dc.subjectDifferential Geometry
dc.subject11F75; 22E40, 57M50
dc.titleOn the non-vanishing of the first Betti number of hyperbolic three manifolds
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