Formal groups and quantum cohomology

Seidel, Paul¹

¹ Department of Mathematics, Massachusetts Insitutute of Technology, Cambridge, MA, United States

Geometry & topology, Tome 27 (2023) no. 8, pp. 2937-3060.

Résumé

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 ${\mathbb{𝔽}}_p$ for some prime $p$, the $p^{\text{ th}}$ 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.

Détail

DOI : 10.2140/gt.2023.27.2937

Classification : 53D37, 53D45, 14L05
Keywords: Steenrod operations, quantum cohomology

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