A spectral sequence to compute L2-Betti numbers of groups and groupoids
- Autores: Roman Sauer, Andreas Thom
- Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 81, Nº 3, 2010, págs. 747-773
- Idioma: inglés
- DOI: 10.1112/jlms/jdq017
- Enlaces
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Resumen
We construct a spectral sequence for L2-type cohomology groups of discrete measured groupoids.
Based on the spectral sequence, we prove the Hopf�Singer conjecture for aspherical manifolds with poly-surface fundamental groups. More generally, we obtain a permanence result for the Hopf�Singer conjecture under taking fiber bundles whose base space is an aspherical manifold with poly-surface fundamental group. As further sample applications of the spectral sequence, we obtain new vanishing theorems and explicit computations of L2-Betti numbers of groups and manifolds and obstructions to the existence of normal subrelations in measured equivalence relations.
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