The cohomology of lattices in SL(2,C)

dc.creatorFinis, Tobias
dc.creatorGrunewald, Fritz
dc.creatorTirao, Paulo
dc.date2008-08-08
dc.date.accessioned2026-07-07T09:55:40Z
dc.date.available2026-07-07T09:55:40Z
dc.descriptionThis paper contains both theoretical results and experimental data on the behavior of the dimensions of the cohomology spaces H^1(G,E_n), where Gamma is a lattice in SL(2,C) and E_n is one of the standard self-dual modules. In the case Gamma = SL(2,O) for the ring of integers O in an imaginary quadratic number field, we make the theory of lifting explicit and obtain lower bounds linear in n. We have accumulated a large amount of experimental data in this case, as well as for some geometrically constructed and mostly non-arithmetic groups. The computations for SL(2,O) lead us to discover two instances with non-lifted classes in the cohomology. We also derive an upper bound of size O(n^2 / log n) for any fixed lattice Gamma in the general case. We discuss a number of new questions and conjectures suggested by our results and our experimental data.
dc.identifierhttps://arxiv.org/abs/0808.1204
dc.identifierhttp://arxiv.org/abs/0808.1204
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/166711
dc.subjectNumber Theory
dc.subject11F75
dc.titleThe cohomology of lattices in SL(2,C)
dc.typetext

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