Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the characteristic classes of actions of lattices in higher rank Lie groups


Author: Garrett Stuck
Journal: Trans. Amer. Math. Soc. 324 (1991), 181-200
MSC: Primary 57R30; Secondary 22E40, 57R20, 58H10
DOI: https://doi.org/10.1090/S0002-9947-1991-0986031-0
MathSciNet review: 986031
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that under certain assumptions, the measurable cohomology class of the linear holonomy cocycle of a foliation yields information about the characteristic classes of the foliation. Combined with the results of a previous paper, this yields vanishing theorems for characteristic classes of certain actions of lattices in higher rank semisimple Lie groups.


References [Enhancements On Off] (What's this?)

  • [B1] R. Bott, On the characteristic classes of groups of diffeomorphisms, Enseign. Math. 23 (1977), 208-220. MR 0488080 (58:7651)
  • [B2] -, On a topological obstruction to integrability, Proc. Sympos. Pure Math., vol. 16, Amer. Math. Soc., Providence, R.I., 1970, pp. 27-36. MR 0266248 (42:1155)
  • [B-H] R. Bott and A. Haefliger, On characteristic classes of $ \Gamma$-foliations, Bull. Amer. Math. Soc. 78 (1972), 1039-1044. MR 0307250 (46:6370)
  • [D] G. Duminy, L'invariant de Godbillon-Vey d'un feuilletage se localise dans les feuilles ressort, preprint (1982).
  • [F-M] J. Feldman and C. C. Moore, Ergodic equivalence relations, cohomology, and von Neumann algebras. I, Trans. Amer. Math. Soc. 234 (1977), 289-323. MR 0578656 (58:28261a)
  • [Ha] A. Haefliger, Sur les classes caractéristiques des feuilletages, Sém. Bourbaki, no. 412 (1971/72).
  • [H-H] J. Heitsch and S. Hurder, Secondary classes, Weil measures and the geometry of foliations, J. Differential Geom. 4 (1984).
  • [H-K] S. Hurder and A. Katok, Ergodic theory and Weil measures for foliations, Ann. of Math. (2) 126 (1987), 221-275. MR 908148 (89d:57042)
  • [K-T] F. Kamber and P. Tondeur, Foliated bundles and characteristic classes, Lecture Notes in Math., Springer-Verlag, New York, 1976. MR 0402773 (53:6587)
  • [K] H. Karcher, Riemannian center of mass and mollifier smoothing, Comm. Pure Appl. Math. 30 (1977), 509-541. MR 0442975 (56:1350)
  • [M] G. A. Margulis, Discrete groups of motions of manifolds of non-positive curvature, Amer. Math. Soc. Transl. 109 (1977), 33-45.
  • [Mo] G. D. Mostow, Some new decomposition theorems for semi-simple groups, Mem. Amer. Math. Soc. 14 (1955), 31-54. MR 0069829 (16:1087g)
  • [R] A. Ramsay, Virtual groups and group actions, Adv. in Math. 6 (1971), 253-322. MR 0281876 (43:7590)
  • [S] G. Stuck, Cocycles of ergodic group actions and vanishing of first cohomology for $ S$-arithmetic groups, preprint. MR 1087799 (92f:22009)
  • [Z1] R. J. Zimmer, Ergodic theory and semisimple groups, Birkhäuser, Boston, Mass., 1984. MR 776417 (86j:22014)
  • [Z2] -, Ergodic actions of semisimple groups and product relations, Ann. of Math. (2) 118 (1983), 9-19. MR 707158 (85b:22013)
  • [Z3] -, On the algebraic hull of an automorphism group of a principal bundle, preprint (January, 1989).

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57R30, 22E40, 57R20, 58H10

Retrieve articles in all journals with MSC: 57R30, 22E40, 57R20, 58H10


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1991-0986031-0
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society