The simplification of singularities of Lagrangian and Legendrian fronts

Daniel Álvarez-Gavela

doi:10.1007/s00222-018-0811-3

The simplification of singularities of Lagrangian and Legendrian fronts

Daniel Álvarez-Gavela

Mathematics

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6 Scopus citations

Abstract

We establish a full h-principle (C⁰-close, relative, parametric) for the simplification of singularities of Lagrangian and Legendrian fronts. More precisely, we prove that if there is no homotopy theoretic obstruction to simplifying the singularities of tangency of a Lagrangian or Legendrian submanifold with respect to an ambient foliation by Lagrangian or Legendrian leaves, then the simplification can be achieved by means of a Hamiltonian isotopy.

Original language	English (US)
Pages (from-to)	641-737
Number of pages	97
Journal	Inventiones Mathematicae
Volume	214
Issue number	2
DOIs	https://doi.org/10.1007/s00222-018-0811-3
State	Published - Nov 1 2018

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00222-018-0811-3

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AB - We establish a full h-principle (C0-close, relative, parametric) for the simplification of singularities of Lagrangian and Legendrian fronts. More precisely, we prove that if there is no homotopy theoretic obstruction to simplifying the singularities of tangency of a Lagrangian or Legendrian submanifold with respect to an ambient foliation by Lagrangian or Legendrian leaves, then the simplification can be achieved by means of a Hamiltonian isotopy.

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The simplification of singularities of Lagrangian and Legendrian fronts

Abstract

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