Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-28T13:42:38.093Z Has data issue: false hasContentIssue false
  • English
  • Français

Generic singularities of symplectic and quasi-symplectic immersions

Published online by Cambridge University Press:  07 June 2013

W. DOMITRZ ,
S. JANECZKO  and
M. ZHITOMIRSKII
W. DOMITRZ
Affiliation:
Warsaw University of Technology, Faculty of Mathematics and Information Science, ul. Koszykowa 75, 00-662 Warsaw, Poland. e-mail: [email protected]
S. JANECZKO
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, P.O. Box 137, 00-950 Warsaw, Poland. Warsaw University of Technology, Faculty of Mathematics and Information Science, ul. Koszykowa 75, 00-662 Warsaw, Poland. e-mail: [email protected]
M. ZHITOMIRSKII
Affiliation:
Department of Mathematics, Technion, 32000 Haifa, Israel. e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

For any k<2n we construct a complete system of invariants in the problem of classifying singularities of immersed k-dimensional submanifolds of a symplectic 2n-manifold at a generic double point.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 155 , Issue 2 , September 2013 , pp. 317 - 329
Copyright
Copyright © Cambridge Philosophical Society 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[Ar1]Arnol'd, V. I.First step of local symplectic algebra, Differential topology, infinite-dimensional Lie algebras, and applications. Amer. Math. Soc. Transl. Ser. 2 194 (44), 1999, 1–8.Google Scholar
[Ar2]Arnol'd, V. I.Mathematical problems in classical physics. Trends and perspectives in applied mathematics 120, Appl. Math. Sci. 100 (Springer, New York, 1994).CrossRefGoogle Scholar
[AG]Arnol'd, V. I. and Givental', A. B.Symplectic geometry, Dynamical systems, IV, Encycl.of Math. Sciences, vol. 4, Springer, Berlin, 2001.Google Scholar
[DJZ1]Domitrz, W., Janeczko, S. and Zhitomirskii, M.Relative Poincare lemma, contractibility, quasi-homogeneity and vector fields tangent to a singular variety. Illinois J. Math. 48, No. 3 (2004), 803–835.CrossRefGoogle Scholar
[DJZ2]Domitrz, W., Janeczko, S. and Zhitomirskii, M.Symplectic singularities of varietes: the method of algebraic restrictions. J. Reine Angew. Math. 618 (2008), 197–235.Google Scholar
[GZ]Gelfand, I. M. and Zakharevich, I. S.Spectral theory of a pencil of third-order skew-symmetric differential operators on s 1. Funct. Anal. Appl. 23 (1989), no. 2, 8593.Google Scholar
[Ma]Martinet, J.Sur les singularites des formes differentielles. Ann. Inst. Fourier 20 (1970), no. 1, 95–178.CrossRefGoogle Scholar
[MR]McRae, A. S.Symplectic geometry for pairs of submanifolds. Rocky Mountain J. Math. 35 (2005), no. 5, 1755–1764.CrossRefGoogle Scholar
[Me]Melrose, R. B.Equivalence of glancing hypersurfaces. Invent. Math. 37 (1976), 165–191.CrossRefGoogle Scholar
[Os]Oshima, T.On analytic equivalence of glancing hypersurfaces. Sci. Pap. Coll. Gen. Educ. Univ. Tokyo 28 (1978), 51–57.Google Scholar
[Zh1]Zhitomirskii, M.Relative Darboux theorem for singular manifolds and local contact algebra. Canadian J. Math. 57, No. 6 (2005), 1314–1340.CrossRefGoogle Scholar
[Zh2]Zhitomirskii, M.Typical singularities of differential 1-forms and Pfaffian equations. Trans. Math. Monog. 113 (Amer. Math. Soc., Providence, RI, 1992).Google Scholar