Pseudo-rotations and Steenrod squares revisited

In this note we prove that if a closed monotone symplectic manifold admits a Hamiltonian pseudo-rotation, which may be degenerate, then the quantum Steenrod square of the cohomology class Poincaré dual to the point must be deformed. This result gives restrictions on the existence of pseudo-rotations, implying a form of uni-ruledness by pseudo-holomorphic spheres, and generalizes a recent result of the author. The new component in the proof consists in an elementary calculation with capped periodic orbits.

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Received 19 January 2020

Accepted 5 September 2020

Published 22 November 2021