| Authors: | Nigel Higson, John Roe and Thomas Schick |
| Title: | Spaces with vanishing l 2-homology and their fundamental groups (after Farber and Weinberger) |
| Publication Information: | Geometriae Dedicata, 87 (2001), 335-343 |
| Abstract: |
The purpose of this note is to prove the following results: Theorem Let G be a finitely presented group and suppose that the homol- ogy of G with coefficients in l 2(G) is zero in degrees 0,1 and 2. Then there is a connected 3-dimensional finite CW-complex X with fundamental group G such that the homology of G with coefficients in l 2(G) is zero in all degrees. Theorem Let G be a finitely presented group and suppose that the homology G with coefficients in l 2(G) is zero in degrees 0,1 and 2. For every dimension n at least 6 there is a closed manifold M of dimension n and with fundamental group G such that the homology of G with coefficients in l 2(G) is zero in all degrees. |