JSJ decomposition for handlebody-knots

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.

arXiv comment28 pages, 12 figures; section reordered for better flow, introduction revised with two corrections in corollaries 1.3, 1.4 of v1 (Corollaries 1.2, 1.3 in v2) made, typos corrected