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

Stuck, Garrett

doi:10.1090/S0002-9947-1991-0986031-0

On the characteristic classes of actions of lattices in higher rank Lie groups
HTML articles powered by AMS MathViewer

by Garrett Stuck

Trans. Amer. Math. Soc. 324 (1991), 181-200

DOI: https://doi.org/10.1090/S0002-9947-1991-0986031-0

PDF | Request permission

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

Raoul Bott, On the characteristic classes of groups of diffeomorphisms, Enseign. Math. (2) 23 (1977), no. 3-4, 209–220. MR 488080
Raoul Bott, On a topological obstruction to integrability, Global Analysis (Proc. Sympos. Pure Math., Vols. XIV, XV, XVI, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 127–131. MR 0266248
R. Bott and A. Haefliger, On characteristic classes of $\Gamma$-foliations, Bull. Amer. Math. Soc. 78 (1972), 1039–1044. MR 307250, DOI 10.1090/S0002-9904-1972-13101-X

L’invariant de Godbillon-Vey d’un feuilletage se localise dans les feuilles ressort

Jacob Feldman and Calvin C. Moore, Ergodic equivalence relations, cohomology, and von Neumann algebras. I, Trans. Amer. Math. Soc. 234 (1977), no. 2, 289–324. MR 578656, DOI 10.1090/S0002-9947-1977-0578656-4

Sur les classes caractéristiques des feuilletages

Secondary classes, Weil measures and the geometry of foliations

4

S. Hurder and A. Katok, Ergodic theory and Weil measures for foliations, Ann. of Math. (2) 126 (1987), no. 2, 221–275. MR 908148, DOI 10.2307/1971401
Franz W. Kamber and Philippe Tondeur, Foliated bundles and characteristic classes, Lecture Notes in Mathematics, Vol. 493, Springer-Verlag, Berlin-New York, 1975. MR 0402773
H. Karcher, Riemannian center of mass and mollifier smoothing, Comm. Pure Appl. Math. 30 (1977), no. 5, 509–541. MR 442975, DOI 10.1002/cpa.3160300502

Discrete groups of motions of manifolds of non-positive curvature

109

G. D. Mostow, Some new decomposition theorems for semi-simple groups, Mem. Amer. Math. Soc. 14 (1955), 31–54. MR 69829
Arlan Ramsay, Virtual groups and group actions, Advances in Math. 6 (1971), 253–322 (1971). MR 281876, DOI 10.1016/0001-8708(71)90018-1
Garrett Stuck, Cocycles of ergodic group actions and vanishing of first cohomology for $S$-arithmetic groups, Amer. J. Math. 113 (1991), no. 1, 1–23. MR 1087799, DOI 10.2307/2374819
Robert J. Zimmer, Ergodic theory and semisimple groups, Monographs in Mathematics, vol. 81, Birkhäuser Verlag, Basel, 1984. MR 776417, DOI 10.1007/978-1-4684-9488-4
Robert J. Zimmer, Ergodic actions of semisimple groups and product relations, Ann. of Math. (2) 118 (1983), no. 1, 9–19. MR 707158, DOI 10.2307/2006951

On the algebraic hull of an automorphism group of a principal bundle