The cohomology of lattices in SL(2,C)
| dc.creator | Finis, Tobias | |
| dc.creator | Grunewald, Fritz | |
| dc.creator | Tirao, Paulo | |
| dc.date | 2008-08-08 | |
| dc.date.accessioned | 2026-07-07T09:55:40Z | |
| dc.date.available | 2026-07-07T09:55:40Z | |
| dc.description | This 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.identifier | https://arxiv.org/abs/0808.1204 | |
| dc.identifier | http://arxiv.org/abs/0808.1204 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166711 | |
| dc.subject | Number Theory | |
| dc.subject | 11F75 | |
| dc.title | The cohomology of lattices in SL(2,C) | |
| dc.type | text |