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Automorphisms of the 3-sphere that preserve spatial graphs and handlebody-knots
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classification
math.GT
keywords
spatialautomorphismsgenusgraphgrouphandlebody-knothandlebody-knotspreserve
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We consider the group of isotopy classes of automorphisms of the 3-sphere that preserve a spatial graph or a handlebody-knot embedded in it. We prove that the group is finitely presented for an arbitrary spatial graph or a reducible handlebody-knot of genus two. We also prove that the groups for "most" irreducible genus two handlebody-knots are finite.
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