Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-22T15:02:27.986Z Has data issue: false hasContentIssue false
  • English
  • Français

First Steps of Local Contact Algebra

Published online by Cambridge University Press:  20 November 2018

V. I. Arnold
V. I. Arnold*
Affiliation:
Steklov Mathematical Institute 8, Gubkina Street, 117966 Moscow, GSP – 1, Russia CEREMADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris, Cedex 16-e, France
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider germs of mappings of a line to contact space and classify the first simple singularities up to the action of contactomorphisms in the target space and diffeomorphisms of the line. Even in these first cases there arises a new interesting interaction of local commutative algebra with contact structure.

Keywords

53D1014B05contact manifoldslocal contact algebraDiraciancontactian
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 51 , Issue 6 , 01 December 1999 , pp. 1123 - 1134
Copyright
Copyright © Canadian Mathematical Society 1999

References

[1] Arnold, V. I., Normal forms for functions near degenerate critical points, theWeyl groups Ak, Dk, Ek and Lagrange singularities. Funct. Anal. Appl. 6(1972), 254–272.Google Scholar
[2] Arnold, V. I., First steps of symplectic topology. RussianMath. Surveys (6) 41(1986), 1–21.Google Scholar
[3] Arnold, V. I., Simple singularities of curves. Proc. Steklov Inst. Math. 226(1999).Google Scholar
[4] Arnold, V. I., First steps of local symplectic algebra. Adv. in (former Soviet)Mathematics, D. Fuchs birthday volume, Providence, AMS, 1999.Google Scholar
[5] Arnold, V. I., Mathematical methods of classical mechancs. Springer-Verlag, 1978.Google Scholar
[6] Arnold, V. I., Wave front evolution and equivariantMorse lemma. Comm. Pure Appl.Math. (6) 29(1976), 557–582.Google Scholar
[7] Arnold, V. I., Indices of singular points of 1-forms on manifolds with boundary, convolution of invariants of groups generated by reflections and singular projections of smooth hypersurfaces. Russian Math. Surveys (2) 34(1979), 1–42.Google Scholar
[8] Arnold, V. I. and Givental, A. B., Symplectic geometry. Encycl. of Math. Sci. 4, Springer, 1980, 4–136.Google Scholar
[9] Givental, A. B., Singular Lagrange varieties and their Lagrange mappings. J. Soviet Math. (4) 52(1990), 3246–3278.Google Scholar