A wild Cantor set as the limit set of a conformal group action on $S^ 3$
Authors:
M. Bestvina and D. Cooper
Journal:
Proc. Amer. Math. Soc. 99 (1987), 623-626
MSC:
Primary 57M30; Secondary 20H10, 30C35, 57S25
DOI:
https://doi.org/10.1090/S0002-9939-1987-0877028-4
MathSciNet review:
877028
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We construct a conformal action of a free group of finite rank on ${S^3}$ whose set of discontinuity $\Lambda$ is a wild Cantor set.
- Vicki Chuckrow, Schottky groups and limits of Kleinian groups, Bull. Amer. Math. Soc. 73 (1967), 139–141. MR 213555, DOI https://doi.org/10.1090/S0002-9904-1967-11685-9
- Michael H. Freedman and Richard Skora, Strange actions of groups on spheres, J. Differential Geom. 25 (1987), no. 1, 75–98. MR 873456
- Bernard Maskit, A characterization of Schottky groups, J. Analyse Math. 19 (1967), 227–230. MR 220929, DOI https://doi.org/10.1007/BF02788719
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Additional Information
Keywords:
Conformal group action,
limit set,
wild Cantor set
Article copyright:
© Copyright 1987
American Mathematical Society
