Abstract
The paper applies the JSJ decomposition and Koda–Ozawa's annulus classification to analyze the annulus configuration in a handlebody-knot exterior. We introduce 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.
Funding Statement
The work was supported by National Sun Yat-sen University and Academia Sinica, and MoST (grant no. 110-2115-M-001-004-MY3), Taiwan.
Citation
Yi-Sheng WANG. "JSJ decomposition for handlebody-knots." J. Math. Soc. Japan 76 (4) 1049 - 1085, October, 2024. https://doi.org/10.2969/jmsj/90869086
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