Invariants l2 de relations d’équivalence et de groupes

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1. [Ada90] S. ADAMS, Trees and amenable equivalence relations, Ergodic Theory Dynamical Systems, 10(1) (1990), 1-14. Zbl0667.28003MR1053796
2. [AS90] S. ADAMS and R. SPATZIER, Kazhdan groups, cocycles and trees, Amer. J. Math., 112(2) (1990), 271-287. Zbl0712.22007MR1047300
3. [Ati76] M. ATIYAH, Elliptic operators, discrete groups and von Neumann algebras, Colloque “Analyse et Topologie” en l’Honneur de Henri Cartan (Orsay, 1974), pp. 43-72. Astérisque, No. 32-33. Paris: Soc. Math. France, 1976. Zbl0323.58015
4. [BCH94] P. BAUM, A. CONNES and N. HIGSON, Classifying space for proper actions and K-theory of group C-algebras, In C-algebras: 1943-1993 (San Antonio, TX, 1993), pp. 240-291. Providence, RI: Amer. Math. Soc., 1994. Zbl0830.46061MR1292018
5. [BV97] M. BEKKA and A. VALETTE, Group cohomology, harmonic functions and the first $L^2$-Betti number, Potential Anal., 6(4) (1997), 313-326. Zbl0882.22013MR1452785
6. [Bor85] A. BOREL, The $L^2$-cohomology of negatively curved Riemannian symmetric spaces, Ann. Acad. Sci. Fenn. Ser. A I Math., 10 (1985), 95-105. Zbl0586.57022MR802471
7. [Bro82] K. BROWN, Cohomology of groups, New York: Springer, 1982. Zbl0584.20036MR672956
8. [CFW81] A. CONNES, J. FELDMAN and B. WEISS, An amenable equivalence relation is generated by a single transformation, Ergodic Theory Dynamical Systems, 1(4), 431-450 (1982), 1981. Zbl0491.28018MR662736
9. [CG86] J. CHEEGER and M. GROMOV, $L^2$-cohomology and group cohomology, Topology, 25(2) (1986), 189-215. Zbl0597.57020MR837621
10. [Co79] A. CONNES, Sur la théorie non commutative de l’intégration, In Algèbres d’opérateurs (Sém., Les Plans-sur-Bex, 1978), pp. 19-143. Lect. Notes 725. Berlin: Springer, 1979. Zbl0412.46053
11. [Co82] A. CONNES, A survey of foliations and operator algebras, In Operator algebras and applications, Part I (Kingston, Ont., 1980), pp. 521-628. Providence, RI: Amer. Math. Soc., 1982. Zbl0531.57023MR679730
12. [CZ89] M. COWLING and R. ZIMMER, Actions of lattices in sp(1,n), Ergodic Theory Dynamical Systems, 9(2) (1989), 221-237. Zbl0681.57026MR1007408
13. [Dix69] J. DIXMIER, Les algèbres d’opérateurs dans l’espace hilbertien (algèbres de von Neumann), Gauthier-Villars Editeur, Paris, 1969. Deuxième édition, revue et augmentée, Cahiers Scientifiques, Fasc. XXV. Zbl0088.32304
14. [Dye59] H. DYE, On groups of measure preserving transformations, I, Amer. J. Math., 81 (1959), 119-159. Zbl0087.11501MR131516
15. [Dye63] H. DYE, On groups of measure preserving transformations, II, Amer. J. Math., 85 (1963), 551-576. Zbl0191.42803MR158048
16. [Eck00] B. ECKMANN, Introduction to l2-methods in topology: reduced l2-homology, harmonic chains, l2-Betti numbers, Israel J. Math., 117 (2000), 183-219. Notes prepared by Guido Mislin. Zbl0948.55006MR1760592
17. [Ele97] G. ELEK, Betti numbers and Euler’s formula for combinatorial foliations, Manuscripta Math., 92(2) (1997), 239-247. Zbl0876.57042
18. [FM77a] J. FELDMAN and C. MOORE, Ergodic equivalence relations, cohomology, and von Neumann algebras, I, Trans. Amer. Math. Soc., 234(2) (1977), 289-324. Zbl0369.22009MR578656
19. [FM77b] J. FELDMAN and C. MOORE, Ergodic equivalence relations, cohomology, and von Neumann algebras, II, Trans. Amer. Math. Soc., 234(2) (1977), 325-359. Zbl0369.22010MR578730
20. [FSZ89] J. FELDMAN, C. SUTHERLAND and R. ZIMMER, Subrelations of ergodic equivalence relations, Ergodic Theory Dynamical Systems, 9(2) (1989), 239-269. Zbl0654.22003MR1007409
21. [Fur99a] A. FURMAN, Gromov’s measure equivalence and rigidity of higher rank lattices, Ann. of Math. (2), 150(3) (1999), 1059-1081. Zbl0943.22013
22. [Fur99b] A. FURMAN, Orbit equivalence rigidity, Ann. of Math. (2), 150(3) (1999), 1083-1108. Zbl0943.22012MR1740985
23. [Gab00a] D. GABORIAU, Coût des relations d’équivalence et des groupes, Invent. Math., 139(1) (2000), 41-98. Zbl0939.28012
24. [Gab00b] D. GABORIAU, Sur la (co-)homologie $L^2$ des actions préservant une mesure. C. R. Acad. Sci. Paris Sér. I Math., 330(5) (2000), 365-370. Zbl0988.37003MR1751672
25. [Gro93] M. GROMOV, Asymptotic invariants of infinite groups. In Geometric group theory, Vol. 2 (Sussex, 1991), pp. 1-295. Cambridge: Cambridge Univ. Press, 1993. Zbl0841.20039MR1253544
26. [Har00] P. DE LA HARPE, Topics in geometric group theory, Chicago, IL: University of Chicago Press, 2000. Zbl0965.20025MR1786869
27. [Hae71] A. HAEFLIGER, Homotopy and integrability, In Manifolds-Amsterdam 1970 (Proc. Nuffic Summer School), pp. 133-163. Berlin: Springer, 1971. Zbl0215.52403MR285027
28. [Hjo02] G. HJORTH, A lemma for cost attained, Manuscrit, 2002. Zbl1101.37004
29. [HL91] J. HEITSCH and C. LAZAROV, Homotopy invariance of foliation Betti numbers, Invent. Math., 104(2) (1991), 321-347. Zbl0756.46040MR1098613
30. [ Jol01] P. JOLISSAINT, Approximation properties for measure equivalent groups, Manuscrit, 2001. 
31. [Kec01] A. KECHRIS, Lectures on costs of equivalence relations and groups, Prépublication Caltech, 2001. 
32. [Kri70] W. KRIEGER, On constructing non-isomorphic hyperfinite factors of type III, J. Functional Analysis, 6 (1970), 97-109. Zbl0209.44601MR259624
33. [Lev95] G. LEVITT, On the cost of generating an equivalence relation, Ergodic Theory Dynam. Systems, 15(6) (1995), 1173-1181. Zbl0843.28010MR1366313
34. [Luc94] W. LÜCK, $L^2$-torsion and 3-manifolds, In Low-dimensional topology (Knoxville, TN, 1992), pp. 75-107. Cambridge, MA: Internat. Press, 1994. Zbl0870.57029MR1316175
35. [Luc98] W. LÜCK, $L^2$ -invariants of regular coverings of compact manifolds and CW-complexes, à paraître in “Handbook of Geometry”, Elsevier, 1998. Zbl1069.57017
36. [Luc98a] W. LÜCK, Dimension theory of arbitrary modules over finite von Neumann algebras and $L^2$-Betti numbers, I, Foundations, J. Reine Angew. Math., 495 (1998), 135-162. Zbl0921.55016MR1603853
37. [Luc98b] W. LÜCK, Dimension theory of arbitrary modules over finite von Neumann algebras and $L^2$-Betti numbers, II, Applications to Grothendieck groups, $L^2$-Euler characteristics and Burnside groups, J. Reine Angew. Math., 496 (1998), 213-236. Zbl1001.55019MR1605818
38. [Moo82] C. MOORE, Ergodic theory and von Neumann algebras, In Operator algebras and applications, Part 2 (Kingston, Ont., 1980), pp. 179-226. Providence, RI: Amer. Math. Soc., 1982. Zbl0524.46045MR679505
39. [MS02] N. MONOD and Y. SHALOM, en préparation. Communication personnelle. 
40. [MvN36] F. MURRAY and J. VON NEUMANN, On rings of operators, Ann. of Math. (2), 37 (1936), 116-229. Zbl0014.16101MR1503275
41. [MvN43] F. MURRAY and J. VON NEUMANN, On rings of operators, IV, Ann. of Math. (2), 44 (1943), 716-808. Zbl0060.26903MR9096
42. [OW80] D. ORNSTEIN and B. WEISS, Ergodic theory of amenable group actions, I, The Rohlin lemma, Bull. Amer. Math. Soc. (N.S.), 2(1) (1980), 161-164. Zbl0427.28018MR551753
43. [Pau99] F. PAULIN, Propriétés asymptotiques des relations d’équivalences mesurées discrètes, Markov Process. Related Fields, 5(2) (1999), 163-200. Zbl0937.28015
44. [Sch87] K. SCHMIDT, Some solved and unsolved problems concerning orbit equivalence of countable group actions, Proceedings of the conference on ergodic theory and related topics, II (Georgenthal, 1986), pp. 171-184, Leipzig: Teubner, 1987. Zbl0646.28009MR931144
45. [Shl99a] D. SHLYAKHTENKO, Free Fisher information with respect to a completely positive map and cost of equivalence relations, MSRI preprint 1999-030, 1999. Zbl0982.46049MR1824202
46. [Shl99b] D. SHLYAKHTENKO, Microstates free entropy and cost of equivalence relations, preprint, http://xxx.lanl.gov/abs/math.OA/9912224. MR1983036
47. [Sun87] V. SUNDER, An invitation to von Neumann algebras, New York: Springer, 1987. Zbl0616.46052MR866671
48. [Zim78] R. ZIMMER, Amenable ergodic group actions and an application to Poisson boundaries of random walks, J. Functional Analysis, 27(3) (1978), 350-372. Zbl0391.28011MR473096
49. [Zim84] R. ZIMMER, Ergodic theory and semisimple groups, Basel: Birkhäuser Verlag, 1984. Zbl0571.58015MR776417

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