Givental group action on Topological Field Theories and homotopy Batalin--Vilkovisky algebras

Abstract

In this paper, we initiate the study of the Givental group action on Cohomological Field Theories in terms of homotopical algebra. More precisely, we show that the stabilisers of Topological Field Theories in genus 0 (respectively in genera 0 and 1) are in one-to-one correspondence with commutative homotopy Batalin--Vilkovisky algebras (respectively wheeled commutative homotopy BV-algebras).

30 pages, final version, to appear in Advances in Mathematics

References in corpus (4)

• Three questions in Gromov-Witten theory
• Quantum BCOV theory on Calabi-Yau manifolds and the higher genus B-model
• The structure of the tautological ring in genus one
• Semi-Classical Quantum Fields Theories and Frobenius Manifolds

Cited by in corpus (7)

• The structure of the tautological ring in genus one
• Toric varieties of Loday's associahedra and noncommutative cohomological field theories
• Givental Action and Trivialisation of Circle Action
• Deformation theory of Cohomological Field Theories
• Generalized cohomological field theories in the higher order formalism
• Two problems in the theory of differential equations
• Cumulants, Koszul brackets and homological perturbation theory for commutative $B{V}_{\infty }$ and $IB{L}_{\infty }$ algebras