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Small energy isotopies of loose Legendrian submanifolds
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abstract
We prove that for a closed Legendrian submanifold $L$ of dimension $n \geq 2$ with a loose chart of size $\eta$, any Legendrian isotopy starting at $L$ can be $C^0$-approximated by a Legendrian isotopy with energy arbitrarily close to $\frac{\eta}{2}$. This in particular implies that the displacement energy of loose displaceable Legendrians is bounded by half the size of its smallest loose chart, which proves a conjecture of Dimitroglou Rizell and Sullivan.
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Cited by 1 Pith paper
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Non-orderability and the contact Hofer norm
Contact Hofer norm bounds, obtained from open books and loose Legendrians, imply non-orderability and resolve the standard S^1 × S^2 case.
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