L2-betti numbers of discrete measured groupoids

International Journal of Algebra and Computation

Volumn 15, Issue 5-6, 2005, Pages 1169-1188

  Sauer, Roman ^a  

^a UNIVERSITY OF MÜNSTER   (Germany)

Author keywords

Discrete measured groupoids; L2 betti numbers; Orbit equivalence; Von Neumann algebras

Indexed keywords

EID: 30344482216     PISSN: 02181967     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218196705002748     Document Type: Conference Paper

References (21)

1. G. Anantharaman-Delaroche and J. Renault, Amenable Groupoids, Monographies de L'Enseignement Mathématique [Monographs of L'Enseignement Mathématique], Vol. 36 (L'Enseignement Mathématique, Geneva, 2000).
2. M. F. Atiyah, Elliptic operators, discrete groups and von Neumann algebras, Astérisque 32-33 (1976) 43-72.
3. H. Cartan and S. Eilenberg, Homological algebra, in Princeton Landmarks in Mathematics (Princeton University Press, Princeton, NJ, 1999).
4. 2 -cohomology and group cohomology, Topology 25 (1986) 189-215.
5. A. Connes, Sur la théorie non commutative de l'intégration, in Algèbres d'opérateurs, Sém., Les Plans-sur-Bex, 1978, Lecture Notes in Mathematics, Vol. 725 (Springer, Berlin, 1979), pp. 19-143.
6. 2-Homology for von Neumann Algebras, arXiv:math.OA/0309343.
7. J. Feldman and C. C. Moore, Ergodic equivalence relations, cohomology, and von Neumann algebras, I, Trans. Amer. Math. Soc. 234(2) (1977) 289-324.
8. J. Feldman and C. C. Moore, Ergodic equivalence relations, cohomology, and von Neumann algebras, II, Trans. Amer. Math. Soc. 234(2) (1977) 325-359.
9. A. Furman, Gromov's measure equivalence and rigidity of higher rank lattices, Ann. Math. (2) 150(3) (1999) 1059-1081.
10. A. Furman, Orbit equivalence rigidity, Ann. Math. (2) 150(3) (1999) 1083-1108.
11. 2 de relations d'équivalence et de groupes, Publ. Math. Inst. Hautes Études Sci. (95) (2002) 93-150.
12. A. S. Kechris, Classical Descriptive Set Theory, Graduate Texts in Mathematics, Vol. 156 (Springer-Verlag, New York, 1995).
13. T. Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics, Vol. 189 (Springer-Verlag, New York, 1999).
14. 2-invariants, Math. Ann. 309(2) (1997) 247-285.
15. 2-Betti numbers. I. Foundations, J. Reine Angew. Math. 495 (1998) 135-162.
16. 2-Euler characteristics and Burnside groups, J. Reine Angew. Math. 496 (1998) 213-236.
17. 2 -Invariants: Theory and Applications to Geometry and K-Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], Vol. 44 (Springer-Verlag, Berlin, 2002).
18. S. Popa, On a class of type Hi factors with Betti numbers invariants, arXiv:math.OA/0209130.
19. R. Sauer, Homological invariants and quasi-isometry, Geom. Funct. Anal., to appear.
20. 2 -invariants of groups and discrete measured groupoids, dissertation, Universität Münster (2003). wwwmath.uni-muenster.de/u/roman.sauer.
21. C. A. Weibel, An Introduction to Homological Algebra (Cambridge University Press, Cambridge, 1994).