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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Handlebody orbifolds and Schottky uniformizations of hyperbolic $ 2$-orbifolds


Authors: Marco Reni and Bruno Zimmermann
Journal: Proc. Amer. Math. Soc. 123 (1995), 3907-3914
MSC: Primary 57M50; Secondary 20H10, 30F10, 30F40, 57M60
MathSciNet review: 1307560
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Abstract: 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. Equivalently, 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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DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1307560-5
PII: S 0002-9939(1995)1307560-5
Keywords: Hyperbolic 2-orbifold, Fuchsian group, Schottky group, handlebody
Article copyright: © Copyright 1995 American Mathematical Society