A construction of the quantum Steenrod squares and their algebraic relations

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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 CPn 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.
Original languageEnglish
Pages (from-to)885-970
JournalGeometry and Topology
Volume24
Issue number2
DOIs
Publication statusPublished - 23 Sep 2020

Keywords

  • Gromov-Witten theory
  • quantum cohomology
  • Steenrod squares
  • symplectic geometry
  • symplectic topology

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