6533b827fe1ef96bd12867c7
RESEARCH PRODUCT
Free vs. Locally Free Kleinian Groups
Pekka PankkaJuan Soutosubject
[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]0209 industrial biotechnologyPure mathematicsMathematics::Dynamical SystemsGeneral MathematicsMathematics::General TopologyGroup Theory (math.GR)02 engineering and technology01 natural sciencesMathematics - Geometric Topology020901 industrial engineering & automationDimension (vector space)[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]FOS: MathematicsLimit (mathematics)topologia0101 mathematicsMathematicsApplied Mathematics010102 general mathematicsryhmäteoriaGeometric Topology (math.GT)16. Peace & justiceMathematics::Geometric TopologyKleinian groupsCantor setTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESHausdorff dimensionComputingMethodologies_DOCUMENTANDTEXTPROCESSINGLimit setMathematics - Group Theorydescription
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 an example of a non-free purely hyperbolic Kleinian group whose limit set is a Cantor set of Hausdorff dimension < < 1 + + ε.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-07-20 |