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Pseudo-rotations and holomorphic curves

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, UC Santa Cruz, Sant Cruz, CA, 95064, USA

    Erman Çineli & Viktor L. Ginzburg

  2. Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA

    Başak Z. Gürel

Authors
  1. Erman Çineli
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  2. Viktor L. Ginzburg
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  3. Başak Z. Gürel
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Correspondence to Viktor L. Ginzburg.

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The work is partially supported by NSF CAREER award DMS-1454342, NSF Grant DMS-1440140 through MSRI (BG) and by Simons Collaboration Grant 581382 (VG).

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Çineli, E., Ginzburg, V.L. & Gürel, B.Z. Pseudo-rotations and holomorphic curves. Sel. Math. New Ser. 26, 78 (2020). https://doi.org/10.1007/s00029-020-00609-y

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