Spaces with vanishing $l\sp 2$-homology and their fundamental groups (after Farber and Weinberger)

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dc.creatorHigson, Nigel
dc.creatorRoe, John
dc.creatorSchick, Thomas
dc.date2009-03-22
dc.date.accessioned2026-07-07T12:55:37Z
dc.date.available2026-07-07T12:55:37Z
dc.descriptionThe "zero in the spectrum conjecture" asserted (in its strongest form) that for any manifold M zero should be in the l2-spectrum of the Laplacian (on forms) of the universal covering of M, i.e. that at least one (unreduced) L2-cohomology group of (the universal covering of) M is non-zero. Farber and Weinberger gave the first counterexamples to this conjecture. In this paper, using their fundamental idea to show the following stronger version of this result: Let G be a finitely presented group and suppose that the homology groups H_k(G,\ell^2(G)) are zero for k=0,1,2. For every dimension n\ge 6 there is a closed manifold M of dimension n and with fundamental group G such that the L2-cohomology of (the universal covering of) M vanishes in all degrees.
dc.description11 pages, 2001 paper with updated references
dc.identifierhttps://arxiv.org/abs/0903.3762
dc.identifierhttp://arxiv.org/abs/0903.3762
dc.identifierGeom. Dedicata 87 (2001), no. 1-3, 335--343
dc.identifierdoi:10.1023/A:1012018013481
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/224308
dc.subjectK-Theory and Homology
dc.subjectAlgebraic Topology
dc.subjectOperator Algebras
dc.subjectSpectral Theory
dc.subject57Q10; 46L99
dc.titleSpaces with vanishing $l\sp 2$-homology and their fundamental groups (after Farber and Weinberger)
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