Free vs. Locally Free Kleinian Groups
classification
🧮 math.GT
math.GR
keywords
freegroupskleiniancantordimensionepsilonhausdorfflimit
read the original 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 $<1+\epsilon$.
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