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
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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.