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Singularities of the projections of n-dimensional knots

Published online by Cambridge University Press:  01 May 1999

EIJI OGASA
EIJI OGASA
Affiliation:
Department of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153, Japan, e-mail: ogasa@ms.u-tokyo.ac.jp
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Abstract

Let n≥5. There is a smoothly knotted n-dimensional sphere in (n+2)-space such that the singular point set of its projection in (n+1)-space consists of double points and that the components of the singular point set are two. (The sphere is knotted in the sense that it does not bound any embedded (n+1)-ball in (n+2)-space.) Furthermore, the projection is not the projection of any unknotted sphere in (n+2)-space. There are two inequivalent embeddings of an n-manifold in (n+2)-space such that the singular point set of the projection of each embedding consists of double points and that the number of components of the singular point set of each embedding is one.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 126 , Issue 3 , May 1999 , pp. 511 - 519
Copyright
The Cambridge Philosophical Society 1999

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Footnotes

This research was partially supported by Research Fellowships of the Promotion of Science for Young Scientists.