Genus two Heegaard splittings of exteriors of 1-genus 1-bridge knots II

الأصل · EN

A knot K is called a 1-genus 1-bridge knot in a 3-manifold M if (M,K) has a Heegaard splitting (V₁,t₁)∪ (V₂,t₂) where Vᵢ is a solid torus and tᵢ is a boundary parallel arc properly embedded in Vᵢ. If the exterior of a knot has a genus 2 Heegaard splitting, we say that the knot has an unknotting tunnel. Naturally the exterior of a 1-genus 1-bridge knot K allows a genus 2 Heegaard splitting, i.e., K has an unknotting tunnel. But, in general, there are unknotting tunnels which are not derived form this procedure. Some of them may be levelled with the torus ∂ V₁=∂ V₂, whose case was studied in our previous paper. In this paper, we consider the remaining case.