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arXiv · 2403.10679

$C^1$-Local Flatness and Geodesics of the Legendrian Spectral Distance

Simon Allais·Pierre-Alexandre Arlove
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Abstract

In this article, we give an explicit computation of the order spectral selectors of a pair of $C^1$-close Legendrian submanifolds belonging to an orderable isotopy class. The $C^1$-local flatness of the spectral distance and the characterisation of its geodesics are deduced. Another consequence is the $C^1$-local coincidence of spectral and Shelukhin-Chekanov-Hofer distances. Similar statements are then deduced for several contactomorphism groups.

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Simon Allais, Pierre-Alexandre Arlove. 2024-03-15. $C^1$-Local Flatness and Geodesics of the Legendrian Spectral Distance. https://arxiv.org/abs/2403.10679

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