Complex Schottky Groups
Classical Schottky groups in PSL(2, C) play a key role in both complex geometry and holomorphic dynamics. On one hand, Köbe’s retrosection theorem says that every compact Riemann surface can be obtained as the quotient of an open set in the Riemann sphere S2 which is invariant under the action of a Schottky group. On the other hand, the limit sets of Schottky groups have rich and fascinating geometry and dynamics, which has inspired much of the current knowledge we have about fractal sets and 1-dimensional holomorphic dynamics.
KeywordsMeromorphic Function Pairwise Disjoint Fundamental Domain Complex Line Kleinian Group
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