Free vs. Locally Free Kleinian Groups

2015/05/30 by Pekka Pankka, Pankka, Pekka, Juan Souto +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Mathematical Dynamics and Fractals

paper · doi:10.48550/arxiv.1506.00156

openalex publication_date 2015/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ε>0 examples of non-free purely hyperbolic Kleinian groups whose limit set is a Cantor set of Hausdorff dimension <1+ε.

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