The ∂-stabilization of a Heegaard splitting with distance at least 6 is unstabilized

Abstract

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

Keywords

Heegaard splitting / Distance / Stabilization

References

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