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Transactions of the American Mathematical Society

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Algebraic hulls and smooth orbit equivalence


Author: Alessandra Iozzi
Journal: Trans. Amer. Math. Soc. 326 (1991), 371-384
MSC: Primary 22D40; Secondary 28D15, 57S99
DOI: https://doi.org/10.1090/S0002-9947-1991-1002921-7
MathSciNet review: 1002921
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Abstract: For $ i = 1,2,$ let $ {\mathcal{F}_i}$ be foliations on smooth manifolds $ {M_i}$ determined by the actions of connected Lie groups $ {H_i}$; we describe here some results which provide an obstruction, in terms of a geometric invariant of the actions, to the existence of a diffeomorphism between the $ \mathcal{F}_i^{\prime}{\text{s}}$.


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  • [Be] D. Benardete, Topological equivalence of flows on homogeneous spaces and divergence of one-parameter subgroups of Lie groups, Trans. Amer. Math. Soc. 306 (1988), 499-528. MR 933304 (89k:58248)
  • [CFW] A. Connes, J. Feldman, and B. Weiss, An amenable equivalence relation is generated by a single transformation, Ergodic Theory Dynamical Systems 1 (1981), 431-450. MR 662736 (84h:46090)
  • [D1] H. A. Dye, On groups of measure preserving transformations. I, Amer. J. Math. 81 (1959), 119-159. MR 0131516 (24:A1366)
  • [D2] -, On groups of measure preserving transformations. II, Amer. J. Math. 85 (1963), 551-576. MR 0158048 (28:1275)
  • [I] A. Iozzi, Invariant geometric structures: a non-linear extension of the Borel density theorem, Amer. J. Math, (to appear). MR 1165356 (93k:22008)
  • [K] W. Krieger, On ergodic flows and the isomorphism of factors, Math. Ann. 223 (1976), 19-70. MR 0415341 (54:3430)
  • [M] B. Marcus, Topological conjugacy of horocycle flows, Amer. J. Math. 88 (1966), 154-178. MR 704217 (85b:58103)
  • [PnZ] P. Pansu and R. J. Zimmer, Rigidity of locally homogeneous metrics of negative curvature on the leaves of a foliation, Israel J. Math. 68 (1989), 56-62. MR 1035880 (91e:58144)
  • [Pr] W. Parry, Metric classification of ergodic nilflows, Amer. J. Math. 88 (1966), 819-829. MR 0284567 (44:1792)
  • [Rm] A. Ramsay, Virtual groups and group actions, Adv. in Math. 6 (1971), 253-322. MR 0281876 (43:7590)
  • [Rt] M. Ratner, Ergodic theory in hyperbolic space, Conference on Modern Analysis and Probability (New Haven, Conn., 1982), R. Beals, A. Beck, A. Bellow and A. Hajian, eds., Contemp. Math., vol. 26, Amer. Math. Soc., Providence, R.I., 1984. MR 737411 (85h:58140)
  • [W1] D. Witte, Zero-entropy affine maps on homogeneous spaces, Amer. J. Math. 109 (1987), 927-961. MR 910358 (88i:28038)
  • [W2] -, Topological equivalence of foliations of homogeneous spaces, Trans. Amer. Math. Soc. 317 (1990), 143-166. MR 942428 (90d:22012)
  • [Z1] R. J. Zimmer, Orbit spaces of unitary representations, ergodic theory and simple Lie groups, Ann. of Math. 106 (1977), 573-588. MR 0466406 (57:6286)
  • [Z2] -, Strong rigidity for ergodic actions of semisimple Lie groups, Ann. of Math. 112 (1980), 511-529. MR 595205 (82i:22011)
  • [Z3] -, On the cohomology of ergodic group actions, Israel J. Math. 35 (1980), 289-300. MR 594334 (81m:22011)
  • [Z4] -, Orbit equivalence and rigidity of ergodic actions of Lie groups, Ergodic Theory Dynamical Systems 1 (1981), 237-253. MR 661822 (84a:22019)
  • [Z5] -, Ergodic theory and semisimple groups, Birkhäuser, Boston, Mass., 1984.
  • [Z6] -, Ergodic theory and the automorphism group of a $ G$-structure, Group Representations, Ergodic Theory, Operator Algebras, and Mathematical Physics, Ed., C. C. Moore, Springer-Verlag, New York, 1987. MR 880380 (88f:53060)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1991-1002921-7
Article copyright: © Copyright 1991 American Mathematical Society

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