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On the self-intersections of an immersed sphere

Published online by Cambridge University Press:  17 April 2009

Albert Borbély
Albert Borbély
Affiliation:
Department of Mathematics and Computer Science, Kuwait University, Safat 13060, Kuwait, e-mail: borbely@ mcs.sci.kuniv.edu.kw
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A closed curve f: S1 → ℝ2 in general position gives rise to a word whose letters are the self-intersection points, each of them appearing exactly twice. Such a word is called a Gauss code. The problem of determining whether a given Gauss code is realisable or not was first proposed by Gauss and it has been settled a long time ago. The analogous question for immersions f: S2 → ℝ3 in general position is settled only in a special case when the immersion has no triple points. We give a necessary condition for a system of curves to be realisable by a general immersion f: S2 → ℝ3.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 75 , Issue 3 , June 2007 , pp. 453 - 458
Copyright
Copyright © Australian Mathematical Society 2007

References

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