Canceling branch points and cusps on projections of knotted surfaces in  -space |
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| Authors: | Osamu Saeki Yasushi Takeda |
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| Institution: | Faculty of Mathematics, Kyushu University, Hakozaki, Fukuoka 812-8581, Japan ; Graduate School of Mathematics, Kyushu University, Hakozaki, Fukuoka 812-8581, Japan |
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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. |
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| Keywords: | Knotted surface non-orientable surface branch point cusp elimination of singularities |
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