Formal groups and quantum cohomology

Seidel, Paul

doi:10.2140/gt.2023.27.2937

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Formal groups and quantum cohomology

Paul Seidel

Geometry & Topology 27 (2023) 2937–3060

DOI: 10.2140/gt.2023.27.2937

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 $𝔽_{p}$ 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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Volume 27, issue 8 (2023)