Ribbon dioperads and modular ribbon properads

Abstract

We define and study the notions of ribbon dioperads and modular ribbon properads. We give a Lie algebra structure on the colimit total object and the limit total object of a ribbon dioperad, and we give a norm map between them. We give a cobar construction for dg ribbon co-dioperads. We also prove similar results for modular ribbon properads. These results are applied to the study of higher Hochschild cochain complexes and pre-Calabi-Yau categories.