Bulletin of the
Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2009; 46(5): 1019-1029

Printed September 1, 2009

https://doi.org/10.4134/BKMS.2009.46.5.1019

Copyright © The Korean Mathematical Society.

The disjoint curve property and bridge surfaces

Sungbok Hong and Heoung Sook Kim

Korea University and Korea University

Abstract

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We show that every bridge surface of certain types of $(1,1)$ prime knot has the disjoint curve property. Also we determine when a bridge surface of a pretzel knot of type $(-2,3,n)$ has the disjoint curve property.

Keywords: disjoint curve property, bridge surface, $(1,1)$-knot, Heegaard splitting

MSC numbers: Primary 57M99; Secondary 57M27, 57N10

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