JSJ decomposition for handlebody-knots (Q6634725)

Handlebody-knots are an important topic in low dimensional topology and play an important role in the study of \(3\)-manifolds. In the paper under review, the author applies the JSJ decomposition and Koda-Ozawa's annulus classification [\textit{Y. Koda} et al., Trans. Am. Math. Soc. 367, No. 4, 2875--2904 (2015; Zbl 1310.57015)] to analyze the annulus configuration in a handlebody-knot exterior. Also, the author introduces the notion of the annulus diagram, to pack the configuration into a labeled graph, and classify genus two handlebody-knots in terms of their annulus diagrams. Applications to handlebody-knot symmetries are discussed; methods to produce handlebody-knots with various types of annulus diagrams are also presented.