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l1-Homology of Combable Groups and 3-Manifold Groups

S. Gersten asked whether the reduced l1-homology of a group of type ℱn vanishes in all dimensions up to n - 1. We prove this for combable groups and for the fundamental groups of closed 3-manifolds. This means that the l1-homology in these cases can be interpreted as "an amount of non-linearity" for the isoperimetric functions.