Document Zbl 1030.57031

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Heegaard reducing spheres for the 3-sphere. (English) Zbl 1030.57031

Rend. Ist. Mat. Univ. Trieste 32, Suppl. 1, 397-410 (2001).

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.

Reviewer: Vincent Blanloeil (Strasbourg)

Cited in 2 Documents

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

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