Pseudo-rotations and Steenrod squares

Egor Shelukhin

doi:10.3934/jmd.2020010

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2020, Volume 16: 289-304. Doi: 10.3934/jmd.2020010

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Pseudo-rotations and Steenrod squares

Egor Shelukhin

Department of Mathematics and Statistics, University of Montreal, C.P. 6128 Succ. Centre-Ville Montreal, QC H3C 3J7, Canada

Received: September 02, 2019

Revised: July 2020

Published: October 2020

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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.

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Mathematics Subject Classification: Primary: 53D40, 37J10; Secondary: 37J45.

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