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<p>In this paper, we prove that the Ham-orbit space from a fiber of a large family of cotangent bundles, as a metric space with respect to the Floertheoretic 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 [8], to Liouville domains. Then we modify Usher’s constructions in [21, 22] (which were used to obtain Hofer-large scale geometric properties) to achieve our desired conclusions.</p>

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Spectrally-large scale geometry in cotangent bundles

  • 期刊论文

  • 发表日期：

    2026年5月25日

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  • Qi Feng,
  • Jun Zhang

摘要

In this paper, we prove that the Ham-orbit space from a fiber of a large family of cotangent bundles, as a metric space with respect to the Floertheoretic 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 [8], to Liouville domains. Then we modify Usher’s constructions in [21, 22] (which were used to obtain Hofer-large scale geometric properties) to achieve our desired conclusions.