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- W3021643583 abstract "This chapter discusses discontinuous groups. A group of mappings of H onto itself is called discontinuous in H if for every 3 of H, the set of images of 3 has no limit point in H. Because H can be covered by a countable number of compact domains, the number of elements of a discontinuous group is either finite or countably infinite. A group of matrices with real or complex elements is called discrete if every infinite sequence of different matrices diverges. It is obvious that a discontinuous group of symplectic matrices is discrete. For arbitrary n, a discontinuous group Δ is of the first kind if there exists a fundamental domain F with the following three properties: (1) every compact domain in H is covered by a finite number of images of F, (2) only a finite number of images of F are neighbors of F, and (3) the integral converges. In the classical case, the fundamental polygon F is compact if and only if all vertices are elliptic. It is well-known that the uniformization of any field of algebraic functions of genus p > 1 leads to a discontinuous group with the required property." @default.
- W3021643583 created "2020-05-13" @default.
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- W3021643583 date "1943-01-01" @default.
- W3021643583 modified "2023-09-27" @default.
- W3021643583 title "DISCONTINUOUS GROUPS" @default.
- W3021643583 doi "https://doi.org/10.1016/b978-1-4832-3276-8.50008-1" @default.
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