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Versal topological stratification and the bifurcation geometry of map-germs of the plane

Published online by Cambridge University Press:  24 October 2008

J. H. Rieger
J. H. Rieger
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL
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Extract

The set of critical values of a map of the plane (of corank 1) can be regarded as the apparent contour of a smooth surface. It is a classical result of Whitney[13] that generically the apparent contour is a smooth fold curve with isolated cusps and transverse fold crossings. More recent classifications of smooth map-germs of the plane of low codimension (occurring in generic 2- or 3-parameter families), e.g. in [1, 5, 7], were motivated by a question in differential geometry: given any smooth surface which is generically embedded in ℝ3, produce a list of all possible (orthogonal or central) projections of such a surface.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 107 , Issue 1 , January 1990 , pp. 127 - 147
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

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