References
M. Atiyah,Elliptic operators, discrete groups and von Neumann algebras, Astérisque32 (1976), 43–72.
M. Burger and A. Valette,Idempotents in complex group rings: theorems of Zalesskii and Bass revisited, Journal of Lie Theory8 (1998), 219–228.
J. Cheeger and M. Gromov,L 2-cohomology and group cohomology, Topology25 (1986), 189–215.
J. Dodziuk,De Rham-Hodge theory for L 2-cohomology of infinite coverings, Topology16 (1977), 157–165.
J. Dodziuk and V. Mathai,Approximating L 2 invariants of amenable covering spaces: a combinatorial approach, Journal of Functional Analysis154 (1998), 359–378.
B. Eckmann,Harmonische Funktionen und Randwertaufgaben in einem Komplex, Commentarii Mathematici Helvetici17 (1944/45), 240–255.
B. Eckmann,Coverings and Betti numbers, Bulletin of the American Mathematical Society55 (1949), 95–101.
B. Eckmann,Amenable groups and Euler characteristics, Commentarii Mathematici Helvetici67 (1992), 383–393.
B. Eckmann,Manifolds of even dimension with amenable fundamental group, Commentarii Mathematici Helvetici69 (1994), 501–511.
B. Eckmann,4-manifolds, group invariants, and ℓ 2-Betti numbers, L’Enseignement Mathématiques43 (1997), 271–279.
B. Eckmann and P. Linnell,Poincaré duality groups of dimension two, II, Commentarii Mathematici Helvetici58 (1983), 111–114.
B. Eckmann and H. Müller,Poincaré duality groups of dimension two, Commentarii Mathematici Helvetici55 (1980), 510–520.
M. S. Farber,Novikov-Shubin invariants and Morse inequalities, Geometric and Functional Analysis6 (1996), 628–665.
E. Følner,On groups with full Banach mean value, Mathematica Scandinavica3 (1955), 336–354.
R. I. Grigorchuk,An example of a finitely presented amenable group that does not belong to the class EG, Matematicheskii Sbornik189 (1998), no. 1, 79–100.
J.-C. Hausmann and S. Weinberger,Caractéristique d’Euler et groupes fondamentaux des variétés de dimension 4, Commentarii Mathematici Helvetici60 (1985), 139–144.
P. Linnell,Division rings and group von Neumann algebras, Forum Mathematicum5 (1993), 561–576.
W. Lück,L 2-Betti numbers of mapping tori and groups, Topology33 (1994), 203–214.
W. Lück,Hilbert modules over finite von Neumann algebras and applications to L 2-invariants, Mathematische Annalen309 (1997), 247–285.
F. J. Murray and J. von Neumann,On rings of operators, Annals of Mathematics (2)37 (1936), 116–229.
S. P. Novikov and M. A. Shubin,Morse inequalities and von Neumann invariants of nonsimply connected manifolds, Uspekhi Matematicheskikh Nauk41 (1986), 222–223.
A. L. Paterson,Amenability, Mathematical Surveys and Monographs 29, American Mathematical Society, 1988.
A. E. Zalesskii,On a problem of Kaplansky, Soviet Mathematics13 (1972), 449–452.
Author information
Authors and Affiliations
Corresponding author
Additional information
Notes by Guido Mislin, based on lectures by Beno Eckmann, autumn 1997, at the Mathematical Research Institute, ETH Zurich.
Rights and permissions
About this article
Cite this article
Eckmann, B. Introduction to ℓ2-methods in topology: Reduced ℓ2-homology, harmonic chains, ℓ2-betti numbers. Isr. J. Math. 117, 183–219 (2000). https://doi.org/10.1007/BF02773570
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02773570