Small-energy isotopies of loose Legendrian submanifolds

Nakamura, Lukas

doi:10.2140/gt.2024.28.4233

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Small-energy isotopies of loose Legendrian submanifolds

Lukas Nakamura

Geometry & Topology 28 (2024) 4233–4255

DOI: 10.2140/gt.2024.28.4233

Abstract

We prove that for a closed Legendrian submanifold $L$ of dimension $n \geq 2$ with a loose chart of size $η$ , any Legendrian isotopy starting at $L$ can be $C^{0}$ –approximated by a Legendrian isotopy with energy arbitrarily close to $\frac{1}{2} η$ . 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 (2020).

Keywords

Legendrian submanifolds, loose Legendrians, Shelukhin–Chekanov–Hofer energy, displacement of Legendrian submanifolds

Mathematical Subject Classification

Primary: 53D10

References

Publication

Received: 4 August 2021

Revised: 30 January 2023

Accepted: 6 May 2023

Published: 27 December 2024

Proposed: Yakov Eliashberg

Seconded: Leonid Polterovich, Dmitri Burago

Authors

Lukas Nakamura
Department of Mathematics Uppsala University Uppsala Sweden

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Volume 28, issue 9 (2024)