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Formal groups and quantum cohomology

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arxiv 1910.08990 v2 pith:QPNRJRFW submitted 2019-10-20 math.SG math.AGmath.AT

Paul Seidel This is my paper · ORCID
classification math.SGmath.AGmath.AT
keywords formalcohomologygroupgroupsmanifoldquantumalgebraarithmetic
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 1 Pith paper

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  1. Advancements in Functorial Homological Mirror Symmetry

    hep-th 2025-02 reject novelty 4.0 of 10

    A programmatic review asserting that stability and transversality in Donaldson-Thomas degeneracy formulas correspond to abelian versus nonabelian gauging in Rozansky-Witten theory, without providing a derivation.

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