Pseudo-rotations and holomorphic curves

• Erman Çineli ^[2] ; Viktor L. Ginzburg ^[2] ; Basak Z. Gürel ^[1]
  1. [1] University of Central Florida

     University of Central Florida

     Estados Unidos

     
  2. [2] UC Santa Cruz, USA
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 5, 2020
• Idioma: inglés
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• Resumen

  • We prove a variant of the Chance–McDuff conjecture for pseudo-rotations: under certain additional conditions, a closed symplectic manifold which admits a Hamiltonian pseudo-rotation must have deformed quantum product and, in particular, some non-zero Gromov–Witten invariants. The only assumptions on the manifold are that it is weakly monotone and that its minimal Chern number is at least two. The conditions on the pseudo-rotation are expressed in terms of the linearized flow at one of the fixed points and are hypothetically satisfied for most (but not all) pseudo-rotations.