OCHA and the swiss-cheese operad

In this paper we show that the relation between Kajiura-Stasheff’s OCHA and A. Voronov’s swiss-cheese operad is analogous to the relation between SH Lie algebras and the little discs operad. More precisely, we show that the OCHA operad is quasi-isomorphic to the operad of top-dimensional homology classes of the swiss-cheese operad.