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Complex Schottky Groups

  • Angel Cano
  • Juan Pablo Navarrete
  • José Seade
Chapter
Part of the Progress in Mathematics book series (PM, volume 303)

Abstract

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.

Keywords

Meromorphic Function Pairwise Disjoint Fundamental Domain Complex Line Kleinian Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Angel Cano
    • 1
  • Juan Pablo Navarrete
    • 2
  • José Seade
    • 1
  1. 1.Instituto de MatemáticasUniversidad Nacional Autónoma de México Unidad CuernavacaCuernavacaMexico
  2. 2.Facultad de MatemáticasUniversidad Autónoma de YucatánMéridaMexico

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