Mathematical Research Letters

Volume 28 (2021)

Number 4

Pseudo-rotations and Steenrod squares revisited

Pages: 1255 – 1261



Egor Shelukhin (Department of Mathematics and Statistics, University of Montreal, Canada)


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.

Received 19 January 2020

Accepted 5 September 2020

Published 22 November 2021