Arithmeticity of holonomy groups of Lie foliations

Arithmeticity of holonomy groups of Lie foliations
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J. Amer. Math. Soc. 1 (1988), 35-58

DOI: https://doi.org/10.1090/S0894-0347-1988-0924701-4

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References

Hyman Bass, Finitely generated subgroups of $\textrm {GL}_{2}$, The Smith conjecture (New York, 1979) Pure Appl. Math., vol. 112, Academic Press, Orlando, FL, 1984, pp. 127–136. MR 758465, DOI 10.1016/S0079-8169(08)61638-4
Robert A. Blumenthal, Transversely homogeneous foliations, Ann. Inst. Fourier (Grenoble) 29 (1979), no. 4, vii, 143–158 (English, with French summary). MR 558593
Armand Borel, Density properties for certain subgroups of semi-simple groups without compact components, Ann. of Math. (2) 72 (1960), 179–188. MR 123639, DOI 10.2307/1970150
Yves Carrière, Feuilletages riemanniens à croissance polynômiale, Comment. Math. Helv. 63 (1988), no. 1, 1–20 (French). MR 928025, DOI 10.1007/BF02566750
Étienne Ghys and Yves Carrière, Relations d’équivalence moyennables sur les groupes de Lie, C. R. Acad. Sci. Paris Sér. I Math. 300 (1985), no. 19, 677–680 (French, with English summary). MR 802650
A. Connes, J. Feldman, and B. Weiss, An amenable equivalence relation is generated by a single transformation, Ergodic Theory Dynam. Systems 1 (1981), no. 4, 431–450 (1982). MR 662736, DOI 10.1017/s014338570000136x

Structures feuilletees

Yves Carrière, Flots riemanniens, Astérisque 116 (1984), 31–52 (French). Transversal structure of foliations (Toulouse, 1982). MR 755161
Edmond Fedida, Sur les feuilletages de Lie, C. R. Acad. Sci. Paris Sér. A-B 272 (1971), A999–A1001 (French). MR 285025
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
Jacob Feldman, Peter Hahn, and Calvin C. Moore, Orbit structure and countable sections for actions of continuous groups, Adv. in Math. 28 (1978), no. 3, 186–230. MR 492061, DOI 10.1016/0001-8708(78)90114-7
Étienne Ghys, Groupes d’holonomie des feuilletages de Lie, Nederl. Akad. Wetensch. Indag. Math. 47 (1985), no. 2, 173–182 (French). MR 799078
André Haefliger, Structures feuilletées et cohomologie à valeur dans un faisceau de groupoïdes, Comment. Math. Helv. 32 (1958), 248–329 (French). MR 100269, DOI 10.1007/BF02564582
Bertram Kostant, On the existence and irreducibility of certain series of representations, Bull. Amer. Math. Soc. 75 (1969), 627–642. MR 245725, DOI 10.1090/S0002-9904-1969-12235-4

Discrete groups of motions of manifolds of non-positive curvature

109

G. A. Margulis, Finiteness of quotient groups of discrete subgroups, Funktsional. Anal. i Prilozhen. 13 (1979), no. 3, 28–39 (Russian). MR 545365
Pierre Molino, Géométrie globale des feuilletages riemanniens, Nederl. Akad. Wetensch. Indag. Math. 44 (1982), no. 1, 45–76 (French). MR 653455
Calvin C. Moore, Amenable subgroups of semisimple groups and proximal flows, Israel J. Math. 34 (1979), no. 1-2, 121–138 (1980). MR 571400, DOI 10.1007/BF02761829
M. S. Raghunathan, Discrete subgroups of Lie groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 68, Springer-Verlag, New York-Heidelberg, 1972. MR 0507234
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
Georges Reeb, Sur certaines propriétés topologiques des variétés feuilletées, Publ. Inst. Math. Univ. Strasbourg, vol. 11, Hermann & Cie, Paris, 1952 (French). MR 0055692
Bruce L. Reinhart, Foliated manifolds with bundle-like metrics, Ann. of Math. (2) 69 (1959), 119–132. MR 107279, DOI 10.2307/1970097
Klaus Schmidt, Cocycles on ergodic transformation groups, Macmillan Lectures in Mathematics, Vol. 1, Macmillan Co. of India, Ltd., Delhi, 1977. MR 0578731

The geometry and topology of

-manifolds

Robert J. Zimmer, Amenable ergodic group actions and an application to Poisson boundaries of random walks, J. Functional Analysis 27 (1978), no. 3, 350–372. MR 0473096, DOI 10.1016/0022-1236(78)90013-7
Robert J. Zimmer, Strong rigidity for ergodic actions of semisimple Lie groups, Ann. of Math. (2) 112 (1980), no. 3, 511–529. MR 595205, DOI 10.2307/1971090
Robert J. Zimmer, Orbit equivalence and rigidity of ergodic actions of Lie groups, Ergodic Theory Dynam. Systems 1 (1981), no. 2, 237–253. MR 661822, DOI 10.1017/s0143385700009251
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
R. J. Zimmer, Kazhdan groups acting on compact manifolds, Invent. Math. 75 (1984), no. 3, 425–436. MR 735334, DOI 10.1007/BF01388637
C. C. Moore (ed.), Group representations, ergodic theory, operator algebras, and mathematical physics, Mathematical Sciences Research Institute Publications, vol. 6, Springer-Verlag, New York, 1987. MR 880370, DOI 10.1007/978-1-4612-4722-7
Robert J. Zimmer, Amenable actions and dense subgroups of Lie groups, J. Funct. Anal. 72 (1987), no. 1, 58–64. MR 883503, DOI 10.1016/0022-1236(87)90081-4