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Equivariant images of projective space under the action of SL (n, ℤ)

Published online by Cambridge University Press:  19 September 2008

Robert J. Zimmer
Robert J. Zimmer
Affiliation:
Department of Mathematics, University of Chicago, Chicago, Illinois 60637, USA
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The point of this note is to answer in the affirmative a question of G. A. Margulis. In the course of his proof of the finiteness of either the cardinality or the index of a normal subgroup of an irreducible lattice in a higher rank semi-simple Lie group [3], [4], Margulis proves that if Γ = SL (n, ℤ), n≥3, (X, μ) is a measurable Γ-space, μ quasi-invariant, and φ: ℙn−1→X is a measure class preserving Γ-map, then either φ is a measure space isomorphism or μ is supported on a point. Margulis then asks whether the topological analogue of this result is true. This is answered in the following.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 1 , Issue 4 , December 1981 , pp. 519 - 522
Copyright
Copyright © Cambridge University Press 1981

References

REFERENCES

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