TY - JOUR
T1 - The simplification of singularities of Lagrangian and Legendrian fronts
AU - Álvarez-Gavela, Daniel
N1 - Funding Information:
I am very grateful to my advisor Yasha Eliashberg for insightful guidance throughout this project. I would also like to thank Laura Starkston for reading carefully the first draft of this paper and offering numerous remarks and corrections which have greatly improved the exposition. I am indebted to the ANR Microlocal group who held a workshop in January 2017 to dissect an early version of the paper and in particular to Sylvain Courte and Alexandre Vérine who spotted several mistakes in the proof of the local wrinkling lemma and made useful suggestions for fixing them. My gratitude also goes to Roger Casals, Sander Kupers, Emmy Murphy, Oleg Lazarev and Kyler Siegel for many helpful discussions surrounding the general notion of flexibility. Finally, many thanks to the referee for numerous helpful comments and corrections. The author was partially supported by NSF Grant DMS-1505910.
Funding Information:
The author was partially supported by NSF Grant DMS-1505910.
Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2018/11/1
Y1 - 2018/11/1
N2 - 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.
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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U2 - 10.1007/s00222-018-0811-3
DO - 10.1007/s00222-018-0811-3
M3 - Article
AN - SCOPUS:85051674579
VL - 214
SP - 641
EP - 737
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
SN - 0020-9910
IS - 2
ER -