#### Volume 12, issue 2 (2012)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
Inequivalent handlebody-knots with homeomorphic complements

### Jung Hoon Lee and Sangyop Lee

Algebraic & Geometric Topology 12 (2012) 1059–1079
##### Abstract

We distinguish the handlebody-knots ${5}_{1},{6}_{4}$ and ${5}_{2},{6}_{13}$ in the table, due to Ishii et al, of irreducible handlebody-knots up to six crossings. Furthermore, we construct two infinite families of handlebody-knots, each containing one of the pairs ${5}_{1},{6}_{4}$ and ${5}_{2},{6}_{13}$, and show that any two handlebody-knots in each family have homeomorphic complements but they are not equivalent.

##### Keywords
handlebody-knot, essential annuli
Primary: 57M50
##### Publication
Received: 31 October 2011
Revised: 20 February 2012
Accepted: 21 February 2012
Published: 7 May 2012
##### Authors
 Jung Hoon Lee Department of Mathematics and Inst. of Pure and Applied Math. Chonbuk National University Jeonju 561-756 Korea Sangyop Lee Department of Mathematics Chung-Ang University 221 Heukseok-dong, Dongjak-gu Seoul 156-756 South Korea