Canceling branch points and cusps on projections of knotted surfaces in $4$-space
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- by Osamu Saeki and Yasushi Takeda PDF
- Proc. Amer. Math. Soc. 132 (2004), 3097-3101 Request permission
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.References
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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
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 3097-3101
- MSC (2000): Primary 57Q45; Secondary 57R45
- DOI: https://doi.org/10.1090/S0002-9939-04-07487-8
- MathSciNet review: 2063132