# zbMATH — the first resource for mathematics

Heegaard reducing spheres for the 3-sphere. (English) Zbl 1030.57031
In a previous paper with W. Thurston the author defined an invariant in $${\mathbb Q}/2$$ of a knot with unknotting tunnel $$\gamma$$. To construct this invariant they characterized reducing spheres for genus two Heegaard splittings of $$S^3$$.
In the paper under review the author generalizes this characterisation to arbitrary genus Heegaard splittings of $$S^3$$ and proves that there always exists a sequence of complete collections of reducing spheres with some conditions.

##### MSC:
 57N12 Topology of the Euclidean $$3$$-space and the $$3$$-sphere (MSC2010) 57N10 Topology of general $$3$$-manifolds (MSC2010)
##### Keywords:
Heegaard spliting; reducing sphere; 3-sphere