Affine Schottky Groups and Crooked Tilings

Details Affine Schottky Groups and Crooked Tilings Affine Schottky Groups and Crooked Tilings

2010-05-08

arxiv.org/abs/1005.1315v1

Contemporary Mathematics 262 (2000), pp. 69--90

Mathematics

Differential Geometry

This paper appeared in the Contemporary Mathematics volume, "Crystallographic groups and their generalizations", the proceedin

Scientific paper

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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