On characteristic numbers of 24 dimensional string manifolds (Q5918617)

This paper is concerned with \(24\)-dimensional string manifolds. The authors construct an explicit isomorphism from the \(24\)-dimensional string cobordism group \(\Omega_{24}^{\mathrm{String}}\) to \(\mathbb{Z}\oplus\mathbb{Z}\oplus\mathbb{Z}\oplus\mathbb{Z}\) and find representatives of an integral basis of \(\Omega_{24}^{\mathrm{String}}\). Then they obtain various results on the divisibility of characteristic numbers of \(24\)-dimensional string manifolds, such as \(2\)-primary divisibility of signature and modified signature, \(3\)-primary divisibility of twisted signature, etc. Editorial remark: This article is identical with [Zbl 1487.57035].