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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 51,64 and 52,613 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 51,64 and 52,613, and show that any two handlebody-knots in each family have homeomorphic complements but they are not equivalent.

Keywords
handlebody-knot, essential annuli
Mathematical Subject Classification 2010
Primary: 57M50
References
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