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arXiv · 2401.17590

Spectrally-large scale geometry in cotangent bundles

Qi Feng·Jun Zhang
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Abstract

In this paper, we prove that the ${\rm Ham}$-orbit space from a fiber of a large family of cotangent bundles, as a metric space with respect to the Floer-theoretic spectral metric, contains a quasi-isometric embedding of an infinite-dimensional normed vector space. The same conclusion holds for the group of compactly supported Hamiltonian diffeomorphisms of some cotangent bundles. To prove this, we generalize a result, relating boundary depth and spectral norm for closed symplectic manifolds in Kislev-Shelukhin's recent work, to Liouville domains. Then we modify Usher's constructions (which were used to obtain Hofer-large scale geometric properties) to achieve our desired conclusions.

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Qi Feng, Jun Zhang. 2024-01-31. Spectrally-large scale geometry in cotangent bundles. https://arxiv.org/abs/2401.17590

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