In this note we prove that if a closed monotone symplectic manifold $ M $ of dimension $ 2n $, satisfying a homological condition that holds in particular when the minimal Chern number is $ N>n $, admits a Hamiltonian pseudo-rotation, then the quantum Steenrod square of the point class must be deformed. This gives restrictions on the existence of pseudo-rotations. Our methods rest on previous work of the author, Zhao, and Wilkins, going back to the equivariant pair-of-pants product-isomorphism of Seidel.
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