No 2-knot has triple point number two or three
Shin Satoh
Source: Osaka J. Math. Volume 42, Number 3
(2005), 543-556.
Abstract
It is known that a 2-knot has the triple point number less than two if and only if it is of ribbon-type. We prove that there is no 2-knot of triple point number two or three. Hence the 2-twist-spun trefoil, which is known as a 2-knot of triple point number four, is one of the simplest non-ribbon 2-knots.
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Permanent link to this document: http://projecteuclid.org/euclid.ojm/1153494501
Mathematical Reviews number (MathSciNet): MR2166721
Zentralblatt MATH identifier: 1088.57018
2012 © Osaka University and Osaka City University, Departments of Mathematics
Osaka Journal of Mathematics
