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Mathematics  2010 

Affine Schottky Groups and Crooked Tilings

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Abstract:

In his 1990 doctoral thesis, Todd Drumm showed that proper affine deformations of free Fuchsian groups could be constructed as Schottky groups using a new family of hypersurfaces called "crooked planes." The existence of proper affine deformations of Fuchsian Schottky groups was demonstrated by Margulis in the early 1980's, answering a question raised by Milnor in 1977. This paper expounds Drumm's result, at least in the case of Fuchsian Schottky groups (that is, when the group contains no parabolic elements).

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