On the integral cohomology of Bianchi groups. (English) Zbl 1269.22007
Summary: Extensive and systematic machine computations are carried out to investigate the integral cohomology of the Euclidean Bianchi groups and their congruence subgroups. The collected data give insight into several aspects, including the asymptotic behavior of the torsion in the first homology. Along with the experimental work, some basic properties of the integral cohomology are recorded with an eye toward the liftability issue of Hecke eigenvalue systems.
MSC:
| 22E40 | Discrete subgroups of Lie groups |
| 11F41 | Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces |
| 11F75 | Cohomology of arithmetic groups |
| 20H10 | Fuchsian groups and their generalizations (group-theoretic aspects) |
| 20J06 | Cohomology of groups |
Software:
MagmaReferences:
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