Givental Action and Trivialisation of Circle Action

Abstract

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.

26 pages. Substantially changed version containing an extra section

References in corpus (3)

• Pre-Lie deformation theory
• De Rham cohomology and homotopy Frobenius manifolds
• Givental group action on Topological Field Theories and homotopy Batalin--Vilkovisky algebras

Cited by in corpus (6)

• Pre-Lie deformation theory
• Toric varieties of Loday's associahedra and noncommutative cohomological field theories
• Deformation theory of Cohomological Field Theories
• Categorical Enumerative Invariants, II: Givental formula
• Generalized cohomological field theories in the higher order formalism
• The Deligne-Mumford operad as a trivialization of the circle action