Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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BICOMPRESSIBLE SURFACES AND INCOMPRESSIBLE SURFACES

  • Saito, Toshio (Department of Mathematics Joetsu University of Education)
  • Received : 2018.04.19
  • Accepted : 2018.10.11
  • Published : 2019.03.31
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Abstract

We give new evidence that "complicated" Heegaard surfaces behave like incompressible surfaces. More precisely, suppose that a closed connected orientable 3-manifold M contains a closed connected incompressible surface F which separates M into two (connected) components $M_1$ and $M_2$. Let S be a Heegaard surface of M. Our result is that if the Hempel distance of S is at least four, then S is isotoped so that $S{\cap}M_i$ is incompressible for each i = 1, 2.

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