勒让德子流形的 $C^0$-极限与正环路
辛几何
2025-03-19 v4
摘要
我们证明，若一个勒让德子流形在一个同胚映射下的像光滑，且该同胚是一列切触同胚的 -极限，则该像仍为勒让德子流形。在证明过程中，我们展示了切触流形的任何非勒让德子流形都允许一个正环路，并对 Rosen--Zhang 关于非勒让德子流形的 Chekanov--Hofer--Shelukhin 伪范数退化性的结果给出了一个参数化改进。
引用
@article{arxiv.2212.09190,
title = {$C^0$-limits of Legendrians and positive loops},
author = {Georgios Dimitroglou Rizell and Michael G. Sullivan},
journal= {arXiv preprint arXiv:2212.09190},
year = {2025}
}
备注
V2: Added two references and Remark 2.7. V3: Removed one lemma in Section 3.2, resulting in slightly adjusted subsequent lemmas from that section. V4: Weakened Theorem C to closed Legendrians