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A Lagrangian Klein bottle

Published online by Cambridge University Press:  24 October 2008

J. Hayden  and
E. C. Zeeman
J. Hayden
Affiliation:
University of Warwick
E. C. Zeeman
Affiliation:
University of Warwick
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Extract

Lagrangian theory (2) and elementary catastrophe theory (5) coincide locally but differ globally. Locally the singularities that occur in the two theories are the same, but globally the manifolds that occur are different. We shall show that Lagrangian manifolds are more general.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 2 , March 1981 , pp. 193 - 200
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

REFERENCES

(1)Arnold, V. I.Characteristic class entering in quantization conditions. Func. Anal. Appl. 1 (1967), 1–13.CrossRefGoogle Scholar
(2)Arnold, V. I.Normal forms for functions near degenerate critical points, the Weyl groups of Ak, Dk, Ek and Lagrangian singularities. Func. Anal. Appl. 6 (1973), 254–272.CrossRefGoogle Scholar
(3)Behrend, F. A.A representation of the Klein bottle. J. London Math. Soc. 37 (1962), 432.Google Scholar
(4)Hayden, J. Some global properties of singularities. (Thesis, Warwick University, 1980).Google Scholar
(5)Thom, R. Structural stability and morphogenesis (Translated from the French by D. H. Fowler). (Reading, Mass. Benjamin 1975).Google Scholar
(6)Wall, C. T. C. Geometric properties of generic differentiable manifolds. Geometry and Topology (Lectures Notes in Mathematics 597 (Berlin, Springer 1976)).Google Scholar
(7)Weinstein, A.Lectures on symplectic manifolds. CBMS Regional Conf. Ser. in Math., Amer. Math. Soc, Providence, R.I., no. 29, 1977.Google Scholar