Bull. Korean Math. Soc. 2019; 56(2): 515-520
Online first article October 29, 2018 Printed March 1, 2019
https://doi.org/10.4134/BKMS.b180383
Copyright © The Korean Mathematical Society.
Toshio Saito
Joetsu University of Education
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
Supported by: This work is supported by JSPS KAKENHI Grant Number 15K04869
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd