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Inequivalent handlebody-knots with homeomorphic complements. (English) Zbl 1242.57010
Summary: We distinguish the handlebody-knots \(5_1,6_4\) and \(5_2,6_{13}\) in the table, due to Ishii et al, of irreducible handlebody-knots up to six crossings. Furthermore, we construct two infinite families of handlebody-knots, each containing one of the pairs \(5_1,6_4\) and \(5_2,6_{13}\), and show that any two handlebody-knots in each family have homeomorphic complements but they are not equivalent.

MSC:
57M50 General geometric structures on low-dimensional manifolds
57M25 Knots and links in the \(3\)-sphere (MSC2010)
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