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 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 Full-Text :