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The \(\partial\)-stabilization of a Heegaard splitting with distance at least 6 is unstabilized. (English) Zbl 1297.57034

Summary: Let \(M\) be a compact orientable 3-manifold with \(\partial M\) connected. If \(V\cup_SW\) is a Heegaard splitting of \(M\) with distance at least 6, then the \(\partial\)-stabilization of \(V\cup_SW\) along \(\partial M\) is unstabilized. Hence \(M\) has at least two unstabilized Heegaard splittings with different genera. The basic tool is a result on the disk complex given by Masur and Schleimer.

MSC:

57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
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