Annex: Some additions to the article of Max Karoubi (Q1011931)

This work is a companion of the paper of \textit{M. Karoubi} [Pure Appl. Math. Q. 5, No.~1, 1--68 (2009; Zbl 1184.55003)]. If \(X\) is a simplicial set, Karoubi's construction can be limited to differential forms with support \(S\subset {\mathbb Z}\). Denote by \({\mathcal D}_S^*(X)\) the corresponding differential graded algebra. The main result of this paper is the proof that the inclusion \({\mathcal D}_S^*(S^p)\overline{\otimes} {\mathcal D}_S^*(S^q)\hookrightarrow {\mathcal D}_S^*(S^p)\otimes {\mathcal D}_S^*(S^q)\) is a quasi-isomorphism, if \(\text{card}(S)\geq p+q+4\). Mention also that the author uses a theorem of convergence of spectral sequences established by \textit{W. G. Dwyer} [Topology 13, 255--265 (1974; Zbl 0303.55012)] and proves that the convergence still exists without the assumption of connectivity.