S. Gersten asked whether the reduced ℓ 1-homology of a group of type ℱ n 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 ℓ 1-homology in these cases can be interpreted as "an amount of non-linearity" for the isoperimetric functions.
|Original language||English (US)|
|Number of pages||15|
|Journal||International Journal of Algebra and Computation|
|State||Published - 2002|
ASJC Scopus subject areas