Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Kleinian_group |
| gptkbp:application |
used in the study of Riemann surfaces
used in the theory of automorphic functions |
| gptkbp:defines |
A Schottky group is a finitely generated, free, discrete subgroup of PSL(2,C).
|
| gptkbp:field |
gptkb:mathematics
gptkb:hyperbolic_geometry complex analysis geometric group theory |
| gptkbp:generation |
generated by loxodromic Möbius transformations
|
| https://www.w3.org/2000/01/rdf-schema#label |
Schottky groups
|
| gptkbp:namedAfter |
gptkb:Friedrich_Schottky
|
| gptkbp:property |
Schottky groups act on the Riemann sphere.
Schottky groups are examples of Kleinian groups. Schottky groups are free groups. Schottky groups are not cocompact Schottky groups are not elementary groups limit set of a Schottky group is a Cantor set Schottky groups are discrete subgroups of Möbius transformations. |
| gptkbp:relatedTo |
gptkb:Riemann_surfaces
gptkb:Fuchsian_groups gptkb:Möbius_transformations gptkb:automorphic_functions Kleinian groups free groups |
| gptkbp:bfsParent |
gptkb:Fuchsian_groups
|
| gptkbp:bfsLayer |
6
|