Corpus ID: 119320766

Local intersections of Lagrangian manifolds correspond to catastrophe theory

@article{Offen2018LocalIO,
  title={Local intersections of Lagrangian manifolds correspond to catastrophe theory},
  author={Christian Offen},
  journal={arXiv: Symplectic Geometry},
  year={2018}
}

Christian Offen

Published 2018

Mathematics

arXiv: Symplectic Geometry

Two smooth map germs are right-equivalent if and only if they generate two Lagrangian submanifolds in a cotangent bundle which have the same contact with the zero-section. In this paper we provide a reverse direction to this classical result of Golubitsky and Guillemin. Two Lagrangian submanifolds of a symplectic manifold have the same contact with a third Lagrangian submanifold if and only if the intersection problems correspond to stably right equivalent map germs. We, therefore, obtain a… CONTINUE READING

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