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<p>We prove Arnol’d’s chord conjecture for all Legendrian submanifolds of cosphere bundles of closed manifolds isotopic to conormal bundles of closed submanifolds. Our method of proof involves an isomorphism between wrapped Floer cohomology and the homology of a path space with coefficients in a local system and a twisted version of the Hurewicz theorem.</p>

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The chord conjecture for conormal bundles

  • 期刊论文

  • 发表日期：

    2025年5月22日

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  • Filip Broćić,
  • Dylan Cant,
  • Egor Shelukhin

摘要

We prove Arnol’d’s chord conjecture for all Legendrian submanifolds of cosphere bundles of closed manifolds isotopic to conormal bundles of closed submanifolds. Our method of proof involves an isomorphism between wrapped Floer cohomology and the homology of a path space with coefficients in a local system and a twisted version of the Hurewicz theorem.