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The 2-twist-spun trefoil has the triple point number four


Authors: Shin Satoh and Akiko Shima
Journal: Trans. Amer. Math. Soc. 356 (2004), 1007-1024
MSC (2000): Primary 57Q45; Secondary 57Q35
DOI: https://doi.org/10.1090/S0002-9947-03-03181-7
Published electronically: August 25, 2003
MathSciNet review: 1984465
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Abstract: The triple point number of an embedded surface in 4-space is the minimal number of the triple points on all the projection images into 3-space. We show that the 2-twist-spun trefoil has the triple point number four.


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Additional Information

Shin Satoh
Affiliation: Department of Mathematics, Chiba University, Inage, Chiba, 263-8522, Japan
Email: satoh@math.s.chiba-u.ac.jp

Akiko Shima
Affiliation: Department of Mathematics, Tokai University, 1117 Kitakaname, Hiratuka, Kanagawa, 259-1292, Japan
Email: shima@keyaki.cc.u-tokai.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-03-03181-7
Keywords: 2-knot, surface-knot, triple point, cocycle invariant, motion picture
Received by editor(s): October 15, 2001
Received by editor(s) in revised form: July 24, 2002
Published electronically: August 25, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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