Polynomially weighted $\ell^p$-completions and group homology

Alexander Engel; Clara Löh

doi:10.4171/jca/40

JournalsjcaVol. 4, No. 1pp. 87–109

Polynomially weighted $ℓ^{p}$ -completions and group homology

Alexander Engel
Universität Regensburg, Germany
Clara Löh
Universität Regensburg, Germany

$Polynomially weighted $\ell^p$-completions and group homology cover$

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Abstract

We introduce polynomially weighted $ℓ^{p}$ -norms on the bar complex of a finitely generated group. We prove that, for groups of polynomial or exponential growth, the homology of the completed complex does not depend on the value of $p$ in the range $(1, \infty)$ .

Cite this article

Alexander Engel, Clara Löh, Polynomially weighted $ℓ^{p}$ -completions and group homology. J. Comb. Algebra 4 (2020), no. 1, pp. 87–109

DOI 10.4171/JCA/40