Automorphisms of the 3-sphere that preserve spatial graphs and handlebody-knots

Abstract

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.

23 pages, 11 figures; minor changes, typos corrected; to appear in Mathematical Proceedings of the Cambridge Philosophical Society

References in corpus (1)

• Automorphisms of the 3-sphere that preserve a genus two Heegaard splitting

Cited by in corpus (3)

• Disk complexes and genus two Heegaard splittings for non-prime 3-manifolds
• Essential surfaces of non-negative Euler characteristic in genus two handlebody exteriors
• Topological symmetry groups and mapping class groups for spatial graphs