The simplification of singularities of Lagrangian and Legendrian fronts

• 成果类型: Article
• 署名作者: Alvarez-Gavela, Daniel
• 署名单位: Stanford University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-0811-3
• 发表日期: 2018
• 页码: 641-737
• 关键词: directed embeddings; smooth mappings

摘要

We establish a full h-principle (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.