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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Canceling branch points and cusps on projections of knotted surfaces in $4$-space


Authors: Osamu Saeki and Yasushi Takeda
Journal: Proc. Amer. Math. Soc. 132 (2004), 3097-3101
MSC (2000): Primary 57Q45; Secondary 57R45
Published electronically: May 21, 2004
MathSciNet review: 2063132
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Abstract: For a knotted surface in $4$-space, its generic projection into $3$-space has branch points as its singularities, and its successive projection into $2$-space has fold points and cusps as its singularities. In this paper, we show that for non-orientable knotted surfaces, the numbers of branch points and cusps can be minimized by isotopy.


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Additional Information

Osamu Saeki
Affiliation: Faculty of Mathematics, Kyushu University, Hakozaki, Fukuoka 812-8581, Japan
Email: saeki@math.kyushu-u.ac.jp

Yasushi Takeda
Affiliation: Graduate School of Mathematics, Kyushu University, Hakozaki, Fukuoka 812-8581, Japan
Email: takeda@math.kyushu-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07487-8
PII: S 0002-9939(04)07487-8
Keywords: Knotted surface, non-orientable surface, branch point, cusp, elimination of singularities
Received by editor(s): April 9, 2003
Published electronically: May 21, 2004
Additional Notes: The first author was supported in part by Grant-in-Aid for Scientific Research (No. 13640076), the Ministry of Education, Science and Culture, Japan.
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2004 American Mathematical Society