An operator invariant for handlebody-knots

Volume 217 / 2012

Kai Ishihara, Atsushi Ishii Fundamenta Mathematicae 217 (2012), 233-247 MSC: Primary 57M27; Secondary 57M15, 57M25. DOI: 10.4064/fm217-3-3


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 IshiharaDepartment of Mathematics and Information Sciences
    Faculty of Education
    Yamaguchi University
    1677-1 Yoshida
    Yamaguchi 753-8513, Japan
  • Atsushi IshiiInstitute of Mathematics
    University of Tsukuba
    1-1-1 Tennodai
    Tsukuba, Ibaraki 305-8571, Japan

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