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Canceling branch points and cusps on projections of knotted surfaces in  -space
Author(s):
Osamu
Saeki;
Yasushi
Takeda
Journal:
Proc. Amer. Math. Soc.
132
(2004),
3097-3101.
MSC (2000):
Primary 57Q45;
Secondary 57R45
Posted:
May 21, 2004
MathSciNet review:
2063132
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Abstract:
For a knotted surface in  -space, its generic projection into  -space has branch points as its singularities, and its successive projection into  -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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- 1.
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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:
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
Posted:
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 of article:
Copyright
2004,
American Mathematical Society
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