Formal groups and quantum cohomology

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 mod 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.

References in corpus (4)

• Symplectic cohomology and duality for the wrapped Fukaya category
• Arithmetic mirror symmetry for the 2-torus
• Covariant constancy of quantum Steenrod operations
• A compactification of the moduli space of marked vertical lines in ${\mathbb{C}}^2$

Cited by in corpus (6)

• Covariant constancy of quantum Steenrod operations
• Deformation theory of Cohomological Field Theories
• Hamiltonian no-torsion
• Quantum Steenrod operations of symplectic resolutions
• The $\mathbb{Z}/p$-equivariant cohomology of genus zero Deligne-Mumford space with $1+p$ marked points
• Rational Quantum Cohomology of Steenrod Uniruled Manifolds