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

Osamu Saeki; Yasushi Takeda

doi:10.1090/S0002-9939-04-07487-8

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

Osamu Saeki, Yasushi Takeda

Division of Fundamental mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	3097-3101
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	132
Issue number	10
DOIs	https://doi.org/10.1090/S0002-9939-04-07487-8
Publication status	Published - Oct 1 2004

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-04-07487-8

Cite this

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

Abstract

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