Scholarlink

<p>We provide a <i>C</i><sup>0</sup> counterexample to the Lagrangian Arnold conjecture in the cotangent bundle of a closed manifold. Additionally, we prove a quantitative <i>h</i>-principle for subcritical isotropic embeddings in contact manifolds and provide an explicit construction of a contact homeomorphism that takes a subcritical isotropic curve to a transverse one. On the rigid side, we give another proof of the Dimitroglou Rizell and Sullivan theorem which states that Legendrian knots are preserved by contact homeomorphisms, provided their image is smooth. Moreover, our method gives related examples of rigidity in higher dimensions as well.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

New steps in C0 symplectic and contact geometry of smooth submanifolds

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年5月9日

查看全文
  • Maksim Stokić

摘要

We provide a C0 counterexample to the Lagrangian Arnold conjecture in the cotangent bundle of a closed manifold. Additionally, we prove a quantitative h-principle for subcritical isotropic embeddings in contact manifolds and provide an explicit construction of a contact homeomorphism that takes a subcritical isotropic curve to a transverse one. On the rigid side, we give another proof of the Dimitroglou Rizell and Sullivan theorem which states that Legendrian knots are preserved by contact homeomorphisms, provided their image is smooth. Moreover, our method gives related examples of rigidity in higher dimensions as well.