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

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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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116023, Liaoning, China

    Yanqing Zou

  2. School of Mathematical Sciences, Peking University, Beijing, 100080, China

    Qilong Guo

  3. Department of Mathematics, East China Normal University, Shanghai, 200241, China

    Ruifeng Qiu

Authors
  1. Yanqing Zou
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  2. Qilong Guo
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  3. Ruifeng Qiu
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Corresponding author

Correspondence to Yanqing Zou.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11271058, 11171108).

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Zou, Y., Guo, Q. & Qiu, R. The ∂-stabilization of a Heegaard splitting with distance at least 6 is unstabilized. Chin. Ann. Math. Ser. B 35, 557–562 (2014). https://doi.org/10.1007/s11401-014-0847-7

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  • DOI: https://doi.org/10.1007/s11401-014-0847-7

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