Tangential flatness and global rigidity of higher rank lattice actions
Author:
Nantian Qian
Journal:
Trans. Amer. Math. Soc. 349 (1997), 657673
MSC (1991):
Primary 22E40, 58E40
MathSciNet review:
1401783
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Abstract 
References 
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Additional Information
Abstract: We establish the continuous tangential flatness for orientable weakly Cartan actions of higher rank lattices. As a corollary, we obtain the global rigidity of Anosov Cartan actions.
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 [KL1]
 A. Katok and J. Lewis, Local rigidity for certain groups of toral automorphisms, Israel Math. Jour. 75 (1991), 203241. MR 93g:58076
 [KL2]
 , Global rigidity results for lattice actions on tori and new examples of volumepreserving actions, Israel J. Math. 93 (1996), 253280. CMP 96:10
 [KLZ]
 A. Katok, J. Lewis and R. Zimmer, Cocycle superrigidity and Rigidity for lattice actions on tori, Topology 35 (1) (1996), 2738. CMP 96:06
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 J. Lewis, The algebraic hull of the derivative cocycle, Preprint (1993).
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 G. Prasad and M. S. Raghunathan, Cartan subgroups and lattices in semisimple groups, Ann. Math. 96 (1972), 296317. MR 46:1965
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 N. Qian, Anosov automorphisms for nilmanifolds and rigidity of group actions, Ergodic Theory Dynam. Systems 15 (2) (1995), 341359. MR 96g:58147
 [Q2]
 , Smooth conjugacy for Anosov diffeomorphisms and rigidity of Anosov actions of higher rank lattices, Preprint.
 [QZ]
 N. Qian and R.J. Zimmer, Entropy rigidity for semisimple group actions, to appear Israel J. Math.
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 D. Stowe, The stationary set of a group action, Proc. AMS 79 (1980), 139146. MR 81b:57035
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 W. Thurston, The geometry and topology of 3manifolds, Lecture notes, Princeton.
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 H. Weyl, The structure and representation of continuous groups, Institute for Advanced Studies, 1934.
 [Z1]
 R. Zimmer, Orbit equivalence and rigidity of ergodic actions of Lie groups, Erg. Th. & Dyn. Sys. 1 (1981), 237253. MR 84a:22019
 [Z2]
 , Ergodic theory and semisimple groups, Birkhäuser, Boston, 1984. MR 86j:22014
 [Z3]
 , Actions of semisimple groups and discrete subgroups, Proceedings of the International Congress of Mathematicians, Berkeley (1986), 12471258. MR 89j:22024
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 , Actions of simple Lie groups, in Workshop on Lie groups, ergodic theory and geometry and problems in geometric rigidity, 1992.
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Additional Information
Nantian Qian
Affiliation:
Department of Mathematics, Yale University, P.O. Box 208283, New Haven, Connecticut 06520
Email:
qian@math.yale.edu
DOI:
http://dx.doi.org/10.1090/S0002994797018576
PII:
S 00029947(97)018576
Keywords:
Rigidity of group actions,
Lie groups,
dynamical systems
Received by editor(s):
December 13, 1994
Article copyright:
© Copyright 1997
American Mathematical Society
