For finitely generated groups Γ, the isomorphism between the first ℓ p-cohomology _H_1(p)(Γ) and the reduced 1-cohomology with coefficients in ℓ p(Γ) is exploited to obtain vanishing results for _H_1(p)(Γ). The following cases are treated: groups acting on trees, groups with infinite center, wreath products, and lattices in product groups.
Cite this article
Florian Martin, Alain Valette, On the first <em>L<sup>p</sup></em>-cohomology of discrete groups. Groups Geom. Dyn. 1 (2007), no. 1, pp. 81–100DOI 10.4171/GGD/5