Bicompressible surfaces and incompressible surfaces
Bull. Korean Math. Soc. 2019 Vol. 56, No. 2, 515-520
Published online March 1, 2019
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 : Primary 57N10
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