Inequivalent handlebody-knots with homeomorphic complements

Lee, Jung Hoon; Lee, Sangyop

doi:10.2140/agt.2012.12.1059

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Inequivalent handlebody-knots with homeomorphic complements

Jung Hoon Lee and Sangyop Lee

Algebraic & Geometric Topology 12 (2012) 1059–1079

DOI: 10.2140/agt.2012.12.1059

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

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

Volume 12, issue 2 (2012)