Model-categories of coalgebras over operads.
Modular operads with connected sum and Barannikov’s theory
We introduce the connected sum for modular operads. This gives us a graded commutative associative product, and together with the BV bracket and the BV Laplacian obtained from the operadic composition and self-composition, we construct the full Batalin-Vilkovisky algebra. The BV Laplacian is then used as a perturbation of the special deformation retract of formal functions to construct a minimal model and compute an effective action.
Multicategories and varieties of many-sorted algebras.