A handlebody-knot is a handlebody embedded in the 3-sphere. We improve Luo's result about markings on a surface, and show that an IH-move is sufficient to investigate handlebody-knots with spatial trivalent graphs without cut-edges. We also give fundamental moves with a height function for handlebody-tangles, which helps us to define operator invariants for handlebody-knots. By using the fundamental moves, we give an operator invariant.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm217-3-3,
author = {Kai Ishihara and Atsushi Ishii},
title = {An operator invariant for handlebody-knots},
journal = {Fundamenta Mathematicae},
volume = {219},
year = {2012},
pages = {233-247},
zbl = {1319.57013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm217-3-3}
}
Kai Ishihara; Atsushi Ishii. An operator invariant for handlebody-knots. Fundamenta Mathematicae, Tome 219 (2012) pp. 233-247. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm217-3-3/