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Raghunathan’s conjectures for \(SL(2,{\mathbb{R}{}})\). (English) Zbl 0785.22013

Raghunathan conjectured that unipotent orbits in spaces \(G/\Gamma\), where \(\Gamma\) is a lattice in the Lie group \(G\), have closures which are themselves of the form \(H\) modulo a lattice for some closed subgroup \(H\) of \(G\). There is also an analogous measure theoretic conjecture due to Dani and Margulis. The author has proved both of these conjectures. In the paper under review she gives simplified versions of her proofs for the case \(G=SL_ 2(\mathbb{R})\). These results for \(SL_ 2(\mathbb{R})\) were also obtained by other authors.

MSC:

22E40 Discrete subgroups of Lie groups
57S20 Noncompact Lie groups of transformations
22D40 Ergodic theory on groups
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