Lagrangian cobordism and shadow distance in Tamarkin category

• Tomohiro Asano ^[1] ; Yuichi Ike ^[2] ; Wenyuan Li ^[3]
  1. [1] Kyoto University

     Kyoto University

     Kamigyō-ku, Japón

     
  2. [2] Kyushu University

     Kyushu University

     Hakata Ku, Japón

     
  3. [3] University of Southern California

     University of Southern California

     Estados Unidos

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 3, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01034-9
• Enlaces
  • Texto completo
• Resumen

  • We study exact Lagrangian cobordisms between exact Lagrangians in a cotangent bundle in the sense of Arnol’d, using microlocal theory of sheaves.We construct a sheaf quantization for an exact Lagrangian cobordism between Lagrangians with conical ends, prove an iterated cone decomposition of the sheaf quantization for cobordisms with multiple ends, and show that the interleaving distance of sheaves is bounded by the shadow distance of the cobordism. Using the result, we prove a rigidity result on Lagrangian intersection by estimating the energy cost of splitting and connecting Lagrangians through cobordisms.

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