Geodesic
An operator invariant for handlebody-knots
Kai Ishihara 1   ; Atsushi Ishii 2
1 Department of Mathematics and Information Sciences Faculty of Education Yamaguchi University 1677-1 Yoshida Yamaguchi 753-8513, Japan
2 Institute of Mathematics University of Tsukuba 1-1-1 Tennodai Tsukuba, Ibaraki 305-8571, Japan
Fundamenta Mathematicae, Tome 217 (2012) no. 3, pp. 233-247 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm217-3-3
Keywords: handlebody knot handlebody embedded sphere improve luos result about markings surface ih move sufficient investigate handlebody knots spatial trivalent graphs without cut edges fundamental moves height function handlebody tangles which helps define operator invariants handlebody knots using fundamental moves operator invariant

Kai Ishihara  1   ; Atsushi Ishii  2

1 Department of Mathematics and Information Sciences Faculty of Education Yamaguchi University 1677-1 Yoshida Yamaguchi 753-8513, Japan
2 Institute of Mathematics University of Tsukuba 1-1-1 Tennodai Tsukuba, Ibaraki 305-8571, Japan 
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Kai Ishihara; Atsushi Ishii. An operator invariant for handlebody-knots. Fundamenta Mathematicae, Tome 217 (2012) no. 3, pp. 233-247. doi: 10.4064/fm217-3-3

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