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Schottky group
In mathematics, a Schottky group is a special sort of Kleinian group, first studied by .
==Definition==
Fix some point ''p'' on the Riemann sphere. Each Jordan curve not passing through ''p'' divides the Riemann sphere into two pieces, and we call the piece containing ''p'' the "exterior" of the curve, and the other piece its "interior". Suppose there are 2''g'' disjoint Jordan curves ''A''1, ''B''1,..., ''A''''g'', ''B''''g'' in the Riemann sphere with disjoint interiors. If there are Möbius transformations ''T''''i'' taking the outside of ''A''''i'' onto the inside of ''B''''i'', then the group generated by these transformations is a Kleinian group. A Schottky group is any Kleinian group that can be constructed like this.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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