# Pseudo-rotations and Steenrod squares

## TL;DR

This paper establishes that certain symplectic manifolds with specific homological properties cannot admit Hamiltonian pseudo-rotations without deforming the quantum Steenrod square, providing new restrictions on their existence.

## Contribution

It proves that the quantum Steenrod square must be deformed in the presence of Hamiltonian pseudo-rotations on specific monotone symplectic manifolds, revealing new constraints.

## Key findings

- Quantum Steenrod square deformation is necessary for pseudo-rotations.
- Restrictions on pseudo-rotation existence based on homological conditions.
- Method relies on equivariant pair-of-pants product-isomorphism techniques.

## Abstract

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.