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Formal groups and quantum cohomology

Paul Seidel

Geometry & Topology 27 (2023) 2937–3060
Abstract

We use chain-level genus-zero Gromov–Witten theory to associate to any closed monotone symplectic manifold a formal group (loosely interpreted), whose Lie algebra is the odd-degree cohomology of the manifold (with vanishing bracket). When taken with coefficients in 𝔽p for some prime p, the p th power map of the formal group is related to quantum Steenrod operations. The motivation for this construction comes from derived Picard groups of Fukaya categories, and from arithmetic aspects of mirror symmetry.

Keywords
Steenrod operations, quantum cohomology
Mathematical Subject Classification 2010
Primary: 53D37, 53D45
Secondary: 14L05
References
Publication
Received: 21 October 2019
Revised: 14 January 2022
Accepted: 11 February 2022
Published: 9 November 2023
Proposed: Ciprian Manolescu
Seconded: Leonid Polterovich, Yakov Eliashberg
Authors
Paul Seidel
Department of Mathematics
Massachusetts Insitutute of Technology
Cambridge, MA
United States

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