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arXiv · 1606.00861

Conformal symplectic geometry of cotangent bundles

Baptiste Chantraine·Emmy Murphy
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Abstract

We prove a version of the Arnol'd conjecture for Lagrangian submanifolds of conformal symplectic manifolds: a Lagrangian $L$ which has non-zero Morse-Novikov homology for the restriction of the Lee form $\beta$ cannot be disjoined from itself by a $C^0$-small Hamiltonian isotopy. Furthermore for generic such isotopies the number of intersection points equals at least the sum of the free Betti numbers of the Morse-Novikov homology of $\beta$. We also give a short exposition of conformal symplectic geometry, aimed at readers who are familiar with (standard) symplectic or contact geometry.

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BibTeXRIS

Baptiste Chantraine, Emmy Murphy. 2016-06-02. Conformal symplectic geometry of cotangent bundles. https://arxiv.org/abs/1606.00861

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