论文标题
$ c^0 $ Symplectic和Smooth Submanifolds的接触几何形状中的新步骤
New steps in $C^0$ symplectic and contact geometry of smooth submanifolds
论文作者
论文摘要
我们在封闭的歧管的cotangent束中为拉格朗日阿诺德猜想提供了$ c^0 $反例。此外，我们证明了接触歧管中的亚临界各向同性嵌入的定量$ h $原理，并提供了接触同构的明确结构，该构造将亚临界各向同性曲线带到横向曲线。在刚性的一面，我们给出了Dimitroglou Rizell和Sullivan定理\ Cite {RS22}的另一个证明，该{RS22}指出，只要它们的图像光滑，它通过触点同构保留了legendrian结。此外，我们的方法还提供了相关的较高维度刚度的示例。
We provide a $C^0$ 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 which takes a subcritical isotropic curve to a transverse one. On the rigid side, we give another proof of the Dimitroglou Rizell and Sullivan theorem \cite{RS22} 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.
