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arXiv · 1905.07567

Pseudo-rotations and holomorphic curves

Erman Cineli·Viktor L. Ginzburg·Basak Z. Gurel
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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 greater than one. The conditions on the pseudo-rotation are expressed in terms of the linearized flow at one of the fixed points and hypothetically satisfied for most (but not all) pseudo-rotations.

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Erman Cineli, Viktor L. Ginzburg, Basak Z. Gurel. 2019-05-18. Pseudo-rotations and holomorphic curves. https://arxiv.org/abs/1905.07567

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