Quantum BV-manifolds and quasi-Lie bialgebras

Recently S.A. Merkulov, building on work of Losev and Mnëv, established a connection between the homotopy theory of unimodular Lie 1-bialgebras and Batalin-Vilkovisky formalism via the theory of wheeled properads. In this paper we extend this connection to unimodular quasi-Lie 1-bialgebras, thus widening the class of models treatable with the methods of wheeled properads.