On discreteness of commensurators

Mahan, M. J. (2011) On discreteness of commensurators Geometry and Topology, 15 . pp. 331-350. ISSN 1465-3060

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Official URL: http://maths.rkmvu.ac.in/~mahan/commens.pdf


We begin by showing that commensurators of Zariski dense subgroups of isometry groups of symmetric spaces of non-compact type are discrete provided that the limit set on the Furstenberg boundary is not invariant under the action of a (virtual) simple factor. In particular for rank one or simple Lie groups, Zariski dense subgroups with non-empty domain of discontinuity have discrete commensurators. This generalizes a Theorem of Greenberg for Kleinian groups. We then prove that for all finitely generated, Zariski dense, infinite covolume discrete subgroups of Isom(H3), commensurators are discrete. Together these prove discreteness of commensurators for all known examples of finitely presented, Zariski dense, infinite covolume discrete subgroups of Isom(X) for X an irreducible symmetric space of non-compact type.

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ID Code:89534
Deposited On:28 Apr 2012 12:57
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