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Givental action and trivialisation of circle action. (Action de Givental et trivialisation de l’action du cercle.) (English. French summary) Zbl 1331.18010
The authors show that the Givental group action on genus zero cohomological field theories, also known as formal Frobenius manifolds or hypercommutative algebras, naturally arises in the deformation theory of Batalin-Vilkovisky algebras. They prove that the Givental action is equal to an action of the trivialisations of the trivial circle action. This result relies on the equality of two Lie algebra actions coming from two apparently remote domains: geometry and homotopical algebra.
MSC:
18D50 Operads (MSC2010)
18G55 Nonabelian homotopical algebra (MSC2010)
53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
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