A prime decomposition theorem for string links in a thickened surface (Q6648718)

String links can be regarded as a generalization of braids, which removes the requirement of monotonicity. The classification of string links up to link homotopy was completed by Habegger and Lin in 1990. In this paper under review, the authors considered string links in thickened surfaces. As the main result, it was proved that any non-braid string link in a thickened surface admits a unique decomposition up to the order of factors and braid equivalence. This result generalized the result of \textit{R. Blair} et al. proved in [J. Knot Theory Ramifications 24, No. 2, Article ID 1550005, 24 p. (2015; Zbl 1344.57003)], which focused on 2-strand string links in \(D^2\times [0, 1]\).