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Mathematical Research Letters
Volume 28 (2021)
Number 4
Pseudo-rotations and Steenrod squares revisited
Pages: 1255 – 1261
DOI: https://dx.doi.org/10.4310/MRL.2021.v28.n4.a13
Author
Abstract
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