Higson, N., Roe, J. and Schick, T.: Spaces with vanishing L2-cohomology and their fundamental groups (after Farber and Weinberger)

• Author: Nigel Higson, John Roe, and Thomas Schick
• Titel: L2-invisible manifolds (after Farber and Weinberger)
• To appear in Geometriae Dedicata
• Abstract: Following Farber and Weinberger, we prove that whenever the (unreduced) L2-homology of a finitely presented group G vanishes in degrees 0, 1, and 2, then there is a 6-dimensional manifold M whose fundamental group is G, such that the total Laplacian on the universal covering of M is invertible, or in other words, such that the unreduced L2-homology of the covering vanishes in all degrees.