A genus two handlebody-knot is a genus two handlebody embedded in the three-sphere. In this paper, we describe some necessary conditions for a two-component link to be a constituent link of a genus two handlebody-knot. We give a lower bound of the crossing number of constituent links of a genus two handlebody-knot such that two-variable Alexander polynomial of the link is nonzero.
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Shin’ya Okazaki (2024) studied this question.
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