English

JSJ decomposition for handlebody-knots

Geometric Topology 2023-02-01 v2

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.

Cite

@article{arxiv.2205.03547,
  title  = {JSJ decomposition for handlebody-knots},
  author = {Yi-Sheng Wang},
  journal= {arXiv preprint arXiv:2205.03547},
  year   = {2023}
}

Comments

28 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

R2 v1 2026-06-24T11:10:00.667Z