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arXiv · 2203.13172

Inverse reduction inequalities for spectral numbers and applications

Claude Viterbo
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Abstract

Our main result is the proof of an inequality between the spectral numbers of a Lagrangian and the spectral numbers of its reductions, in the opposite direction to the classical inequality (see e.g [Vit92]). This has applications to the "Geometrically bounded Lagrangians are spectrally bounded" conjecture from [Vit08], to the structure of elements in the $\gamma$-completion of the set of exact Lagrangians. We also investigate the local path-connectedness of the set of Hamiltonian diffeomorphisms with the spectral metric.

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Claude Viterbo. 2022-03-24. Inverse reduction inequalities for spectral numbers and applications. https://arxiv.org/abs/2203.13172

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