Knotted handle decomposing spheres for handlebody-knots
Geometric Topology
2012-11-20 v1
Abstract
We show that a handlebody-knot whose exterior is boundary-irreducible has a unique maximal unnested set of knotted handle decomposing spheres up to isotopies and annulus-moves. As an application, we show that the handlebody-knots and are not equivalent. We also show that some genus two handlebody-knots with a knotted handle decomposing sphere can be determined by their exteriors. As an application, we show that the exteriors of and are not homeomorphic.
Cite
@article{arxiv.1211.4458,
title = {Knotted handle decomposing spheres for handlebody-knots},
author = {Atsushi Ishii and Kengo Kishimoto and Makoto Ozawa},
journal= {arXiv preprint arXiv:1211.4458},
year = {2012}
}