Bicompressible surfaces and incompressible surfaces
Bull. Korean Math. Soc.
Published online 2018 Oct 29
Toshio Saito
Joetsu University of Education
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 $i=1,2$.
Keywords : bicompressible surface, incompressible surface, Heegaard surface, Hempel distance
MSC numbers : 57N10
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