OCHA and Leibniz Pairs, towards a Koszul duality

Abstract

In this paper we study the homology of 2 versions of the swiss-cheese operad. We prove that the zeroth homology of these two versions are Koszul operads and relate this to strong homotopy Lebiniz pairs and OCHA, defined by Kajiura and Stasheff.

33 pages, 3 figures, published in LMP under the title: "Open-Closed Homotopy Algebras and Strong Homotopy Leibniz Pairs Through Koszul Operad Theory"

References in corpus (4)

• Koszul duality of operads and homology of partition posets
• Two-colored noncommutative Gerstenhaber formality and infinity Duflo isomorphism
• OCHA and the swiss-cheese operad
• Formality theorem for Hochschild cochains via transfer

Cited by in corpus (8)

• Hydrodynamic Limit For An Active Exclusion Process
• Non-formality of the Swiss-Cheese operad
• Actions of monoidal categories and representations of Cartan type Lie algebras
• Swiss-Cheese operad and Drinfeld center
• On the Spectral Sequence of the Swiss-cheese Operad
• Configuration Spaces of Manifolds with Boundary
• Relative Recognition Principle
• Non-formality of Voronov's Swiss-Cheese operads