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A
construction of the quantum Steenrod squares and their
algebraic relations
Nicholas Wilkins |
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Geometry & Topology 24 (2020) 885–970
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Abstract |
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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 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
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Mathematical Subject Classification 2010
Primary: 53D45
Secondary: 14N35, 55S10
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References |
Publication
Received: 15 May 2018
Revised: 1 September 2019
Accepted: 2 October 2019
Published: 23 September 2020
Proposed: Leonid Polterovich
Seconded: Ralph Cohen, Ciprian Manolescu
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Authors |
| Nicholas Wilkins | |
| School of Mathematics University of Bristol Bristol United Kingdom |
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