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.


57N12 Topology of the Euclidean \(3\)-space and the \(3\)-sphere (MSC2010)
57N10 Topology of general \(3\)-manifolds (MSC2010)