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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.
Kai Ishihara, and Atsushi Ishii. "An operator invariant for handlebody-knots." Fundamenta Mathematicae 217.3 (2012): 233-247. <http://eudml.org/doc/283340>.
@article{KaiIshihara2012, abstract = {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.}, author = {Kai Ishihara, Atsushi Ishii}, journal = {Fundamenta Mathematicae}, keywords = {handlebody-knot; marking; spatial graph; operator invariant}, language = {eng}, number = {3}, pages = {233-247}, title = {An operator invariant for handlebody-knots}, url = {http://eudml.org/doc/283340}, volume = {217}, year = {2012}, }
TY - JOUR AU - Kai Ishihara AU - Atsushi Ishii TI - An operator invariant for handlebody-knots JO - Fundamenta Mathematicae PY - 2012 VL - 217 IS - 3 SP - 233 EP - 247 AB - 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. LA - eng KW - handlebody-knot; marking; spatial graph; operator invariant UR - http://eudml.org/doc/283340 ER -