Symplectic topology and ideal-valued measures

• Adi Dickstein ^[1] ; Leonid Polterovich ^[1] ; Yaniv Ganor ^[2] ; Frol Zapolsky ^[3]
  1. [1] Tel Aviv University

     Tel Aviv University

     Israel

     
  2. [2] Holon Institute of Technology

     Holon Institute of Technology

     Israel

     
  3. [3] MI SANU, Kneza Mihaila 36, Belgrade, Serbia

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 5, 2024
• Idioma: inglés
• DOI: 10.1007/s00029-024-00967-x
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• Resumen

  • We adapt Gromov’s notion of ideal-valued measures to symplectic topology, and use it for proving new results on symplectic rigidity and symplectic intersections. Furthermore, it allows us to discuss three “big fiber theorems”—the Centerpoint Theorem in combinatorial geometry, the Maximal Fiber Inequality in topology, and the Non-displaceable Fiber Theorem in symplectic topology—from a unified viewpoint. Our main technical tool is an enhancement of the symplectic cohomology theory recently developed by Varolgüneş.

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