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math.GT2021
Rigidity and symmetry of cylindrical handlebody-knots
Yi-Sheng Wang
A recent result of Funayoshi-Koda shows that a handlebody-knot of genus two has a finite symmetry group if and only if it is hyperbolic -- the exterior admits a hyperbolic structur…
math.GT2021
Unknotting annuli and handlebody-knot symmetry
Yi-Sheng Wang
By Thurston's hyperbolization theorem, irreducible handlebody-knots are classified into three classes: hyperbolic, toroidal, and atoroidal cylindrical. It is known that a non-trivi…