Existence of nonarithmetic monodromy groups
- 1 October 1981
- journal article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 78 (10) , 5948-5950
- https://doi.org/10.1073/pnas.78.10.5948
Abstract
In an 1885 paper, E. Picard defined a subgroup Τ(Λ) of PU(2,1) generated by monodromies and depending on parameters Λ = (λ1,λ2,λ3,λ4), 0 < λi < 1, < λi < 3, λi + λj ≥ 1, 1 ≤ i < j ≤ 4. The family Τ(Λ) resembles the family of groups Τ([unk]) defined in 1978 but is a different family. In common with the groups Τ([unk]), (i) Τ(Λ) is discrete for a finite number of Λ, (ii) Τ(Λ) is a nonarithmetic lattice for some Λ, and (iii) for all Λ ∈ [unk]4, there is a compact complex surface S(Λ) with π1 [S(Λ)] of finite index in Τ(Λ).Keywords
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