  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).
