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Symplectic T7, T8 singularities and Lagrangian tangency orders

Part of: Symplectic geometry, contact geometry General theory of differentiable manifolds Theory of singularities and catastrophe theory Curves

Published online by Cambridge University Press:  28 August 2012

Wojciech Domitrz  and
Żaneta Trȩbska
Wojciech Domitrz
Affiliation:
Faculty of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00661 Warsaw, Poland (domitrz@mini.pw.edu.pl; ztrebska@mini.pw.edu.pl)
Żaneta Trȩbska
Affiliation:
Faculty of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00661 Warsaw, Poland (domitrz@mini.pw.edu.pl; ztrebska@mini.pw.edu.pl)
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Abstract

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We study the local symplectic algebra of curves. We use the method of algebraic restrictions to classify symplectic T7, T8 singularities. We define discrete symplectic invariants (the Lagrangian tangency orders) and compare them with the index of isotropy. We use these invariants to distinguish symplectic singularities of classical T7 singularity. We also give the geometric description of symplectic classes of the singularity.

Keywords

symplectic manifoldcurveslocal symplectic algebraalgebraic restrictionsrelative Darboux theoremsingularities

MSC classification

Secondary: 53D05: Symplectic manifolds, general 14H20: Singularities, local rings 58K50: Normal forms 58A10: Differential forms
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 3 , October 2012 , pp. 657 - 683
Copyright
Copyright © Edinburgh Mathematical Society 2012

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