l^p-cohomology for groups of type FP_n

Details l^p-cohomology for groups of type FP_n l^p-cohomology for groups of type FP_n

2005-10-31

arxiv.org/abs/math/0511002v2

Mathematics

Functional Analysis

11 pages Two Proofs extended, some smaller changes

Scientific paper

Let G be a group of type FP_n and let p>1. In this paper we show that the reduced l^p-homology of G is dual to the reduced l^q-cohomology for \frac{1}{p}+\frac{1}{q}=1. In our main theorem we show that for a group of type FP_n with a central element of infinite order the reduced l^p-cohomology vanishes. We generalize this fact for groups with infinitely many elements in the center of the group, for groups which are FCC, for groups with infinitely many finite conjugacy classes, for nilpotent groups, and for groups of polynomial growth.

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