Actions of Semisimple Lie Groups on Circle Bundles

Geometriae Dedicata

Volumn 87, Issue 1-3, 2001, Pages 91-121

  Witte, Dave ^a   Zimmer, Robert J ^b  

^a OKLAHOMA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

Circle bundle; Group action; Kazhdan's property T; Measurable cocycle; S arithmatic group; Semisimple Lie group

Indexed keywords

EID: 0042329433     PISSN: 00465755     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1012068331112     Document Type: Article

References (16)

1. Behr, H.: Arithmetic groups over function fields I, J. Reine Angew. Math. 495 (1998), 79-118.
2. Burger, M. and Monod, N.: Bounded cohomology of lattices in higher rank Lie groups, J. Eur. Math. Soc. 1(2) (1999), 199-235; erratum 1(3) (1999), 338.
3. Burger, M. and Monod, N.: Continuous bounded cohomology and applications, Preprint.
4. Burger, M. and Monod, N.: In preparation.
5. Farb, B. and Shalen, P.: Real-analytic actions of lattices, Invent. Math. 135 (1998), 273-296.
6. Ghys, É.: Actions de réseaux sur le cercle, Invent. Math. 137 (1999), 199-231.
7. de la Harpe, P. and Valette, A.: La propriété (T) de Kazhdan pour les groupes localement compacts, Astérisque 175, Soc. Math. France, 1989.
8. Helgason, S.: Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978.
9. Margulis, G.A.: Discrete Subgroups of Semisimple Lie Groups, Springer, New York, 1991.
10. Reeb, G. and Schweitzer, P.: Un théorème de Thurston établi au moyen de l'analyse non standard, In: P. A. Schweitzer (ed.), Differential Topology, Foliations and Gelfand-Fuks Cohomology, Proc. Sympos., Pontifícia Univ. Católica, Rio de Janeiro, January 1976, Lecture Notes in Math. 652, Springer, New York, 1978, p. 138.
11. Schachermayer, W.: Une modification standard de la demonstration non standard de Reeb et Schweitzer, In: P. A. Schweitzer (ed.), Differential Topology, Foliations and Gelfand-Fuks Cohomology, Proc. Sympos., Pontifícia Univ. Católica, Rio de Janeiro, January 1976, Lecture Notes in Math. 652, Springer, New York, 1978, pp. 139-140.
12. Thurston, W.: A generalization of the Reeb stability theorem, Topology 13 (1974), 347-352.
13. Tits, J.: Algebraic and abstract simple groups, Ann. Math. 80 (1964), 313-329.
14. Warner, G.: Harmonic Analysis on Semi-simple Lie Groups I, Springer, New York, 1972.
15. Witte, D.: Arithmetic groups of higher ℚ-rank cannot act on 1-manifolds, Proc. Amer. Math. Soc. 122 (1994), 333-340.
16. Zimmer, R. J.: Ergodic Theory and Semisimple Groups, Birkhäuser, Boston, 1984.