#### Volume 24, issue 2 (2020)

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A construction of the quantum Steenrod squares and their algebraic relations

### Nicholas Wilkins

Geometry & Topology 24 (2020) 885–970
##### Abstract

We construct a quantum deformation of the Steenrod square construction on closed monotone symplectic manifolds, based on the work of Fukaya, Betz and Cohen. We prove quantum versions of the Cartan and Adem relations. We compute the quantum Steenrod squares for all ${ℂℙ}^{n}$ and give the means of computation for all toric varieties. As an application, we also describe two examples of blowups along a subvariety, in which a quantum correction of the Steenrod square on the blowup is determined by the classical Steenrod square on the subvariety.

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##### Keywords
Gromov–Witten theory, quantum cohomology, Steenrod squares, symplectic geometry, symplectic topology
##### Mathematical Subject Classification 2010
Primary: 53D45
Secondary: 14N35, 55S10