Handlebody Orbifolds and Schottky Uniformizations of Hyperbolic 2-orbifolds

نویسندگان

  • MARCO RENI
  • Ronald J. Stern
چکیده

The retrosection theorem says that any hyperbolic or Riemann surface can be uniformized by a Schottky group. We generalize this theorem to the case of hyperbolic 2-orbifolds by giving necessary and sufficient conditions for a hyperbolic 2-orbifold, in terms of its signature, to admit a uniformization by a Kleinian group which is a finite extension of a Schottky group. Equivalent^, the conditions characterize those hyperbolic 2-orbifolds which occur as the boundary of a handlebody orbifold, that is, the quotient of a handlebody by a finite group action.

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تاریخ انتشار 2010