Bounds on the Lagrangian spectral metric in cotangent bundles

  • Paul Biran

    ETH Zürich, Switzerland
  • Octav Cornea

    University of Montréal, Canada
Bounds on the Lagrangian spectral metric in cotangent bundles cover

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Abstract

Let be a closed manifold and a bounded domain in the cotangent bundle of , containing the zero-section. A conjecture due to Viterbo asserts that the spectral metric for Lagrangian submanifolds in that are exact-isotopic to the zero-section is bounded. In this paper we establish an upper bound on the spectral distance between two such Lagrangians , which depends linearly on the boundary depth of the Floer complexes of and , where is a fiber of the cotangent bundle.

Cite this article

Paul Biran, Octav Cornea, Bounds on the Lagrangian spectral metric in cotangent bundles. Comment. Math. Helv. 96 (2021), no. 4, pp. 631–691

DOI 10.4171/CMH/522