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

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

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...

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Veröffentlicht in:Chinese annals of mathematics. Serie B 2014, Vol.35 (4), p.557-562
Hauptverfasser: Zou, Yanqing, Guo, Qilong, Qiu, Ruifeng
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Zusammenfassung: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.
ISSN:0252-9599
1860-6261
DOI:10.1007/s11401-014-0847-7