Functions of a complex variable Riemann surfaces Concept
Schottky group
Summary
A Schottky group is a group of Möbius transformations generated by maps that pair off disjoint discs in the Riemann sphere. It is a Kleinian group that is a free group and has only loxodromic elements besides the identity. The quotient of its domain of discontinuity is a compact Riemann surface. Every compact Riemann surface arises in this way, which gives a concrete way to build them.
Further reading
About this page
| Tag | YBERRJMXT6 |
|---|---|
| URI | m2://YBERRJMXT6 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 30F40, 30F10, 20E05 |
| Same as | |
| Changed | 2 November 2026 |
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