Quelques nouveaux phénomènes de rang 1 pour les groupes de difféomorphismes du cercle

Commentarii Mathematici Helvetici

Volumn 80, Issue 2, 2005, Pages 355-375

  Navas, Andrés ^a,b  

^a INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES   (France)

^b UNIVERSITY OF CHILE   (Chile)

Author keywords

Circle diffeomorphisms; Group cohomology; Rigidity

Indexed keywords

EID: 27844578671     PISSN: 00102571     EISSN: None     Source Type: Journal    
DOI: 10.4171/CMH/17     Document Type: Article

References (41)

1. Bader, U., Shalom, Y., Factor and normal subgroup theorems for lattices in products of groups. Prépublication, 2004.
2. Ballmann, W., Eberlein, P., Fundamental groups of manifolds of nonpositive curvature. J. Differential Geometry 25 (1987), 1-22. Zbl 0701.53070 MR 0873453
3. Benakli, N., Glasner, Y., Automorphisms groups of trees acting locally with affine permutations. Geom. Dedicata 89 (2002), 1-24. Zbl 1001.20018 MR 1890951
4. Burger, M., Monod, N., Bounded cohomology of lattices in higher rank Lie groups. J. Eur. Math. Soc. (JEMS) 1 (1999), 199-235. Zbl 0932.22008 MR 1694584
5. Burger, M., Monod, N., Continuous bounded cohomology and applications to rigidity theory. Geom. Funct. Anal. 12 (2002), 219-280. Zbl 1006.22010 MR 1911660
6. Burger, M., Mozes, S., Lattices in product of trees. Inst. Hautes Études Sci. Publ. Math. 92 (2000), 151-194. Zbl 1007.22013 MR 1839489
7. Candel, A., Conlon, L., Foliations I. Grad. Stud. Math. 23, Amer. Math. Soc., Providence, RI, 2000. Zbl 0936.57001 MR 1732868
8. Casson, A., Jungreis, D., Convergence groups and Seifert fibered 3-manifolds. Invent. Math. 118 (1994), 441-456. Zbl 0840.57005 MR 1296353
9. Chérix, P., Cowling, M., Jolissaint, P., Julg, P., Valette, A., Groups with the Haagerup property. Gromov's a-(T)-menability. Progr. Math. 197, Birkhäuser, Basel 2001. Zbl 1030.43002 MR 1852148
10. de Cornulier, Y., Relative Kazhdan property. Prépublication, 2005.
11. Farb, B., Shalen, P., Real-analytic actions of lattices. Invent. Math. 135 (1998), 273-296. Zbl 0954.22007 MR 1666834
12. Farley, D., A proper isometric action of Thompson group V on Hilbert space. Internat. Math. Res. Notices 45 (2003), 2409-2414. Zbl 02010461 MR 2006480
13. Furman, A., Mostow-Margulis rigidity with locally compact targets. Geom. Funct. Anal. 11 (2001), 30-59. Zbl 0984.22008 MR 1829641
14. Gabai, D., Convergence groups are Fuchsian groups. Ann. of Math. 136 (1992), 447-510. Zbl 0785.57004 MR 1189862
15. Ghys, É., Groups acting on the circle. Enseign. Math. (2) 47 (2001), 329-407. Zbl 1044.37033 MR 1876932
16. Ghys, É., Actions de réseaux sur le cercle. Invent. Math. 137 (1999), 199-231. Zbl 0995.57006 MR 1703323
17. Ghys, É., Sergiescu, V., Sur un groupe remarquable de difféomorphismes du cercle. Comment. Math. Helv. 62 (1987), 185-239. Zbl 0647.58009 MR 0896095
18. de la Harpe, P., Valette, A., La propriété (T) de Kazhdan pour les groupes localement compacts. Astérisque 175 (1989). Zbl 0759.22001 MR 1023471
19. Herman, M., Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. Inst. Hautes Études Sci. Publ. Math. 49 (1979), 5-233. Zbl 0448.58019 MR 0538680
20. Hinkkanen, A., The structure of some quasisymmetric groups. Mem. Amer. Math. Soc. 83 (1990), 87 pp. Zbl 0707.30018 MR 0948926
21. Hinkkanen, A., Uniformly quasisymmetric groups. Proc. London Math. Soc. 51 (1985), 318-338. Zbl 0574.30022 MR 0794115
22. Korevaar, N., Schoen, R., Global existence theorems for harmonic maps to non-locally compact spaces. Comm. Anal. Geom. 5 (1997), 333-387. Zbl 0908.58007 MR 1483983
23. Monod, N., Continuous bounded cohomology of locally compact groups. Lecture Notes in Math. 1758, Springer-Verlag, Berlin 2001. Zbl 0967.22006 MR 1840942
24. Monod, N., Shalom, Y., Cocycle superrigidity and bounded cohomology for negatively curved spaces. J. Differential Geometry 67 (2004), 1-61.
25. Montgomery, D., Zippin, L., Topological Transformation Groups. Interscience Publishers, New York 1955. Zbl 0068.01904 MR 0073104
26. Muller, M., Sur l'approximation et l'instabilité des feuilletages. Texte non publié, 1982.
27. Navas, A., Actions de groupes de Kazhdan sur le cercle. Ann. Sci. École Norm. Sup. 35 (2002), 749-758. Zbl 1028.58010 MR 1951442
28. Navas, A., Groupes de Neretin et propriété (T) de Kazhdan. C. R. Acad. Sci. Paris Sér. I Math. 335 (2002), 789-792. Zbl 1018.22002 MR 1947700
29. Navas, A., Sur les groupes de difféomorphismes du cercle engendrés par des éléments proches des rotations. Enseign. Math. 50 (2004), 29-68. MR 2084334
30. Navas, A., Reduction of cocycles and groups of diffeomorphisms of the circle. À paraître dans Bull. Belgian Math. Soc.
31. Plante, J., Foliations with measure preserving holonomy. Ann. of Math. 102 (1975), 327-361. Zbl 0314.57018 MR 0391125
32. Pressley, A., Segal, G., Loop groups. Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York 1986. Zbl 0618.22011 MR 0900587
33. Rémy, B., Construction de réseaux en théorie de Kac-Moody. C. R. Acad. Sci. Paris Sér. I Math. 6 (1999), 475-478. Zbl 0933.22029 MR 1715140
34. Reznikov, A., Analytic topology of groups, actions, strings and varietes. Chapter 2: A theory of groups acting in the circle. Preprint, August 11 (1999), 59-65. Disponible électroniquement: http://xxx.lpthe.jussieu.fr/find/ math/l/au :+Reznikov_A/0/1/0/all/0/1.
35. Shalom, Y., Rigidity of commensurators and irreducible lattices. Invent. Math. 141 (2000), 1-54. Zbl 0978.22010 MR 1767270
36. Sullivan, D., On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions. In Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference. Ann. of Math. Stud. 97, Princeton University Press, Princeton, N.J., 1981, 465-496. Zbl 0567.58015 MR 0624833
37. Thurston, W., A generalization of Reeb stability theorem. Topology 13 (1974), 347-352. Zbl 0305.57025 MR 0356087
38. 1-structures avec une seule feuille. Astérisque 116 (1984), 222-234. Zbl 0551.57014 MR 0755173
39. Witte, D., Products of similar matrices. Proc. Amer. Math. Soc. 126 (1998), 1005-1015. Zbl 0893.20033 MR 1451837
40. Witte, D., Arithmetic groups of higher ℚ-rank cannot act on 1-manifolds. Proc. Amer. Math. Soc. 122 (1994), 333-340. Zbl 0818.22006 MR 1198459
41. Witte, D., Zimmer, R., Actions of semisimple Lie groups on circle bundles. Geom. Dedicata 87 (2001), 91-121. Zbl 1017.22004 MR 1866844