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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Superrigidity for irreducible lattices and geometric splitting
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by Nicolas Monod PDF
J. Amer. Math. Soc. 19 (2006), 781-814 Request permission


We prove general superrigidity results for actions of irreducible lattices on CAT$(0)$ spaces, first in terms of the ideal boundary, and then for the intrinsic geometry (also for infinite-dimensional spaces). In particular, one obtains a new and self-contained proof of Margulis’ superrigidity theorem for uniform irreducible lattices in non-simple groups. The proofs rely on simple geometric arguments, including a splitting theorem which can be viewed as an infinite-dimensional (and singular) generalization of the Lawson-Yau/Gromoll-Wolf theorem. Appendix A gives a very elementary proof of commensurator superrigidity; Appendix B proves that all our results also hold for certain non-uniform lattices.
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Additional Information
  • Nicolas Monod
  • Affiliation: Department of Mathematics, The University of Chicago, 5734 University Avenue, Chicago, Illinois 60637
  • Address at time of publication: Université de Genève, 2-4, rue du Lièvre, CP 64, CH-1211 Genève 4, Switzerland
  • MR Author ID: 648787
  • Email:
  • Received by editor(s): December 13, 2004
  • Published electronically: March 21, 2006
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 19 (2006), 781-814
  • MSC (2000): Primary 22Exx; Secondary 53Cxx, 20F65
  • DOI:
  • MathSciNet review: 2219304