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arXiv · 2202.07996

New steps in $C^0$ symplectic and contact geometry of smooth submanifolds

Maksim Stokić
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Abstract

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.

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Maksim Stokić. 2022-02-16. New steps in $C^0$ symplectic and contact geometry of smooth submanifolds. https://arxiv.org/abs/2202.07996

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