# Free vs. Locally Free Kleinian Groups

Abstract : We prove that Kleinian groups whose limit sets are Cantor sets of Hausdorff dimension $<1$ are free. On the other hand we construct for any $\epsilon>0$ examples of non-free purely hyperbolic Kleinian groups whose limit set is a Cantor set of Hausdorff dimension $<1+\epsilon$.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-01178620
Contributor : Marie-Annick Guillemer <>
Submitted on : Monday, July 20, 2015 - 2:55:18 PM
Last modification on : Thursday, February 7, 2019 - 3:03:19 PM

### Citation

Pekka Pankka, Juan Souto. Free vs. Locally Free Kleinian Groups. Journal für die Reine und Angewandte Mathematik, 2019, 2019 (746), pp.149-170. ⟨10.1515/crelle-2016-0005⟩. ⟨hal-01178620⟩

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