Givental action and trivialisation of circle action
Copyright policy )Givental action and trivialisation of circle action
In this paper, we 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. We 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.
- Laboratoire Jean-Alexandre Dieudonné France
- Nice Sophia Antipolis University France
- French National Centre for Scientific Research France
- University of Amsterdam Netherlands
- Université Côte d'Azur France
[MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA], Givental action, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], Nonabelian homotopical algebra, circle action, cohomological field theory, Batalin-Vilkovisky algebra, 510, 004, Mathematics - Algebraic Geometry, Mathematics - Quantum Algebra, Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, FOS: Mathematics, Operads, Quantum Algebra (math.QA), Primary 18G55, Secondary 18D50, 53D45, Algebraic Geometry (math.AG), homotopy Lie algebras
[MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA], Givental action, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], Nonabelian homotopical algebra, circle action, cohomological field theory, Batalin-Vilkovisky algebra, 510, 004, Mathematics - Algebraic Geometry, Mathematics - Quantum Algebra, Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, FOS: Mathematics, Operads, Quantum Algebra (math.QA), Primary 18G55, Secondary 18D50, 53D45, Algebraic Geometry (math.AG), homotopy Lie algebras
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