Algebraic hulls and smooth orbit equivalence
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- by Alessandra Iozzi PDF
- Trans. Amer. Math. Soc. 326 (1991), 371-384 Request permission
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 $\mathcal {F}_i’{\text {s}}$.References
- Diego Benardete, Topological equivalence of flows on homogeneous spaces, and divergence of one-parameter subgroups of Lie groups, Trans. Amer. Math. Soc. 306 (1988), no. 2, 499–527. MR 933304, DOI 10.1090/S0002-9947-1988-0933304-3
- 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
- H. A. Dye, On groups of measure preserving transformations. I, Amer. J. Math. 81 (1959), 119–159. MR 131516, DOI 10.2307/2372852
- H. A. Dye, On groups of measure preserving transformations. II, Amer. J. Math. 85 (1963), 551–576. MR 158048, DOI 10.2307/2373108
- Alessandra Iozzi, Invariant geometric structures: a nonlinear extension of the Borel identity theorem, Amer. J. Math. 114 (1992), no. 3, 627–648. MR 1165356, DOI 10.2307/2374772
- Wolfgang Krieger, On ergodic flows and the isomorphism of factors, Math. Ann. 223 (1976), no. 1, 19–70. MR 415341, DOI 10.1007/BF01360278
- Brian Marcus, Topological conjugacy of horocycle flows, Amer. J. Math. 105 (1983), no. 3, 623–632. MR 704217, DOI 10.2307/2374316
- P. Pansu and Robert J. Zimmer, Rigidity of locally homogeneous metrics of negative curvature on the leaves of a foliation, Israel J. Math. 68 (1989), no. 1, 56–62. MR 1035880, DOI 10.1007/BF02764968
- William Parry, Metric classification of ergodic nilflows and unipotent affines, Amer. J. Math. 93 (1971), 819–828. MR 284567, DOI 10.2307/2373472
- 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
- Marina Ratner, Ergodic theory in hyperbolic space, Conference in modern analysis and probability (New Haven, Conn., 1982) Contemp. Math., vol. 26, Amer. Math. Soc., Providence, RI, 1984, pp. 309–334. MR 737411, DOI 10.1090/conm/026/737411
- Dave Witte, Zero-entropy affine maps on homogeneous spaces, Amer. J. Math. 109 (1987), no. 5, 927–961. MR 910358, DOI 10.2307/2374495
- Dave Witte, Topological equivalence of foliations of homogeneous spaces, Trans. Amer. Math. Soc. 317 (1990), no. 1, 143–166. MR 942428, DOI 10.1090/S0002-9947-1990-0942428-5
- Robert J. Zimmer, Orbit spaces of unitary representations, ergodic theory, and simple Lie groups, Ann. of Math. (2) 106 (1977), no. 3, 573–588. MR 466406, DOI 10.2307/1971068
- 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, On the cohomology of ergodic group actions, Israel J. Math. 35 (1980), no. 4, 289–300. MR 594334, DOI 10.1007/BF02760654
- 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 —, Ergodic theory and semisimple groups, Birkhäuser, Boston, Mass., 1984.
- Robert J. Zimmer, Ergodic theory and the automorphism group of a $G$-structure, Group representations, ergodic theory, operator algebras, and mathematical physics (Berkeley, Calif., 1984) Math. Sci. Res. Inst. Publ., vol. 6, Springer, New York, 1987, pp. 247–278. MR 880380, DOI 10.1007/978-1-4612-4722-7_{1}0
Additional Information
- © Copyright 1991 American Mathematical Society
- 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