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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. [ABSTRACT FROM AUTHOR]

In this paper, we prove the main conjecture on g-areas arising from [7]. That conjecture was announced by the first author in 2004. It states that the g-area of any Hamiltonian diffeomorphism ø is equal to the positive Hofer pseudo-distance between ø and the subspace of Hamiltonian diffeomorphisms that can be expressed as a product of at most g commutators. [ABSTRACT FROM AUTHOR]