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A note on Heegaard genus of self-amalgamated 3-manifold

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Abstract

Let M be a connected orientable compact irreducible 3-manifold. Suppose that ∂M consists of two homeomorphic surfaces F 1 and F 2, and both F 1 and F 2 are compressible in M. Suppose furthermore that g(M,F 1) = g(M) + g(F 1), where g(M,F 1) is the Heegaard genus of M relative to F 1. Let M f be the closed orientable 3-manifold obtained by identifying F 1 and F 2 using a homeomorphism f: F 1 → F 2. The authors show that if f is sufficiently complicated, then g(M f ) = g(M,∂M) + 1.

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Authors and Affiliations

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

    Qilong Guo & Yanqing Zou

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

    Ruifeng Qiu

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

Correspondence to Qilong Guo.

Additional information

The first and third authors are supported by the National Natural Science Foundation of China (No. 11271058). The second author is supported by the National Natural Science Foundation of China (No. 11171108).

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Guo, Q., Qiu, R. & Zou, Y. A note on Heegaard genus of self-amalgamated 3-manifold. Chin. Ann. Math. Ser. B 36, 51–56 (2015). https://doi.org/10.1007/s11401-014-0877-1

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  • DOI: https://doi.org/10.1007/s11401-014-0877-1

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