Superrigidity and countable Borel equivalence relations

Annals of Pure and Applied Logic - Tập 120 - Trang 237-262 - 2003
Simon Thomas1
1Mathematics Department, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA

Tài liệu tham khảo

Adams, 1990, Trees and amenable equivalence relations, Ergodic Theory Dyn. Systems, 10, 1, 10.1017/S0143385700005368 Adams, 2002, Containment does not imply Borel reducibility, vol. 58, 1 Adams, 2000, Linear algebraic groups and countable Borel equivalence relations, J. Amer. Math. Soc., 13, 909, 10.1090/S0894-0347-00-00341-6 Bass, 1964, Sous-groupes d'indice fini dans SLn(Z), Bull. Amer. Math. Soc., 70, 385, 10.1090/S0002-9904-1964-11107-1 Bekka, 2000, Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces, vol. 269 Curtis, 1962 Dixon, 1991, Analytic pro-p Groups, vol. 157 Dougherty, 1994, The structure of hyperfinite Borel equivalence relations, Trans. Amer. Math. Soc., 341, 193, 10.1090/S0002-9947-1994-1149121-0 Feldman, 1977, Ergodic equivalence relations, cohomology and von Neumann algebras, I, Trans. Amer. Math. Soc., 234, 289, 10.1090/S0002-9947-1977-0578656-4 Furman, 1999, Gromov 's measure equivalence and rigidity of higher rank lattices, Ann. Math., 150, 1059, 10.2307/121062 Furman, 1999, Orbit equivalence rigidity, Ann. Math., 150, 1083, 10.2307/121063 Gefter, 1996, Outer automorphism group of the ergodic equivalence relation generated by translations of dense subgroup of compact group on its homogeneous space, Publ. RIMS, Kyoto Univ., 32, 517, 10.2977/prims/1195162855 Gefter, 1988, Fundamental groups for ergodic actions and actions with unit fundamental groups, Publ. RIMS, Kyoto Univ., 24, 821, 10.2977/prims/1195173929 S. Jackson, A.S. Kechris, A. Louveau, Countable Borel equivalence relations, J. Math. Logic, to appear. Kechris, 1992, Countable sections for locally compact group actions, Ergodic Theory and Dynamical Systems, 12, 283, 10.1017/S0143385700006751 Kechris, 1995 Onishchik, 2000, Lie Groups and Lie Algebras II, vol. 21 Platonov, 1994 Ratner, 1991, On Raghunathan's measure conjecture, Ann. Math., 134, 545, 10.2307/2944357 Srivastava, 1998, A Course on Borel Sets, vol. 180 S. Thomas, On the complexity of the classification problem for torsion-free abelian groups of rank two, Acta Math., to appear. S. Thomas, The classification problem for torsion-free abelian groups of finite rank, 2000, preprint. Thomas, 2002, Some applications of superrigidity to Borel equivalence relations, vol. 58, 129 Zimmer, 1984