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arXiv · 1909.11967

From pseudo-rotations to holomorphic curves via quantum Steenrod squares

Erman Cineli·Viktor L. Ginzburg·Basak Z. Gurel
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Abstract

In the context of symplectic dynamics, pseudo-rotations are Hamiltonian diffeomorphisms with finite and minimal possible number of periodic orbits. These maps are of interest in both dynamics and symplectic topology. We show that a closed, monotone symplectic manifold, which admits a non-degenerate pseudo-rotation, must have a deformed quantum Steenrod square of the top degree element, and hence non-trivial holomorphic spheres. This result (partially) generalizes a recent work by Shelukhin and complements the results by the authors on non-vanishing Gromov-Witten invariants of manifolds admitting pseudo-rotations.

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Erman Cineli, Viktor L. Ginzburg, Basak Z. Gurel. 2019-09-26. From pseudo-rotations to holomorphic curves via quantum Steenrod squares. https://arxiv.org/abs/1909.11967

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