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Lagrangian and Legendrian Singularities

  • Victor V. Goryunov
  • V. M. Zakalyukin
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

These are notes of the introductory courses on the subject we lectured in Trieste in 2003 and Luminy in 2004. The lectures contain basic notions and fundamental theorems of the local theory.

Keywords

Symplectic and contact geometry Lagrangian and Legendrian submanifolds and singularities generating family 

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References

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    V.I. Arnold, Singularities of caustics and wave fronts, Kluwer Academic Publ., Dordrecht-Boston-London, 1990.Google Scholar
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    V.I. Arnold, V.V. Goryunov, O.V. Lyashko and V.A. Vassiliev, Singularities II. Classification and Applications, Encyclopaedia of Mathematical Sciences, vol. 39, Dynamical Systems VIII, Springer Verlag, Berlin a.o., 1993.Google Scholar
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    V.I. Arnold, S.M. Gusein-Zade and A.N. Varchenko, Singularities of Differentiable maps. Vol. I, Monographs in Mathematics 82, Birkhäuser, Boston, 1985.zbMATHGoogle Scholar
  4. [4]
    D. McDuff and D. Salomon, Introduction to symplectic topology, Springer Verlag, 1995.Google Scholar
  5. [5]
    C. Viterbo, Generating functions, symplectic geometry and applications, Proc. Intern. Congr. Math., Zurich, 1994.Google Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Victor V. Goryunov
    • 1
  • V. M. Zakalyukin
    • 2
  1. 1.Department of Mathematical SciencesUniversity of LiverpoolLiverpoolUK
  2. 2.Department of Mechanocs and MathematicsMoscow State UniversityMoscowRussia

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