Limit set intersection theorems for Kleinian groups and a conjecture of Susskind
Limit set intersection theorems for Kleinian groups and a conjecture of Susskind
Susskind's conjecture claims that for subgroups $\Phi$ and $\Theta$ of a Kleinian group $\Gamma$ acting on ${\mathbb H}^n$, we have that $\Lambda_c(\Phi)\cap \Lambda_c (\Theta)\subset \Lambda(\Phi\cap\Theta)$, where $\Lambda_c(\Phi)$ is the set of conical limit points of $\Phi$ and $\Lambda(\Phi)$ is the limit set of $\Phi$. We show that Susskind's conjecture largely holds for purely loxodromic Kleinian groups and we present two examples to illustrate that Susskind's conjecture is nearly optimal.
453-464
Anderson, James W.
739c0e33-ef61-4502-a675-575d08ee1a98
June 2014
Anderson, James W.
739c0e33-ef61-4502-a675-575d08ee1a98
Anderson, James W.
(2014)
Limit set intersection theorems for Kleinian groups and a conjecture of Susskind.
Computational Methods and Function Theory, 14 (2-3), .
(doi:10.1007/s40315-014-0078-7).
Abstract
Susskind's conjecture claims that for subgroups $\Phi$ and $\Theta$ of a Kleinian group $\Gamma$ acting on ${\mathbb H}^n$, we have that $\Lambda_c(\Phi)\cap \Lambda_c (\Theta)\subset \Lambda(\Phi\cap\Theta)$, where $\Lambda_c(\Phi)$ is the set of conical limit points of $\Phi$ and $\Lambda(\Phi)$ is the limit set of $\Phi$. We show that Susskind's conjecture largely holds for purely loxodromic Kleinian groups and we present two examples to illustrate that Susskind's conjecture is nearly optimal.
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Submitted date: 28 September 2013
Accepted/In Press date: January 2014
Published date: June 2014
Organisations:
Pure Mathematics
Identifiers
Local EPrints ID: 358054
URI: http://eprints.soton.ac.uk/id/eprint/358054
ISSN: 1617-9447
PURE UUID: 3d6c3a8d-adf1-402f-b94c-0ba1f3c73812
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Date deposited: 09 Oct 2013 10:43
Last modified: 15 Mar 2024 02:52
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