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Horospherically invariant measures and finitely generated Kleinian groups
Author(s) -
Or Landesberg
Publication year - 2021
Publication title -
journal of modern dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.668
H-Index - 25
eISSN - 1930-532X
pISSN - 1930-5311
DOI - 10.3934/jmd.2021012
Subject(s) - mathematics , ergodic theory , invariant (physics) , centralizer and normalizer , psl , finitely generated abelian group , pure mathematics , combinatorics , mathematical physics
Let \begin{document}$ \Gamma < {\rm{PSL}}_2( \mathbb{C}) $\end{document} be a Zariski dense finitely generated Kleinian group. We show all Radon measures on \begin{document}$ {\rm{PSL}}_2( \mathbb{C}) / \Gamma $\end{document} which are ergodic and invariant under the action of the horospherical subgroup are either supported on a single closed horospherical orbit or quasi-invariant with respect to the geodesic frame flow and its centralizer. We do this by applying a result of Landesberg and Lindenstrauss [ 18 ] together with fundamental results in the theory of 3-manifolds, most notably the Tameness Theorem by Agol [ 2 ] and Calegari-Gabai [ 10 ].

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