A construction of the quantum Steenrod squares and their algebraic relations

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.

arXiv comment68 pages, 13 figures. v3: paper as accepted for publication by Geometry & Topology after peer review, uploaded as per MSP open-access policy. Changes: the title is now correctly capitalised. Updated contact details in the paper. Multiple small changes were made across the paper since v2, mainly to make the exposition clearer

References in corpus (1)

• Floer homology of families I

Cited by in corpus (7)

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• Foundational aspects of spinor structures and exotic spinors