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 (9)

• Deformation quantization of Poisson manifolds, I
• Operads and Motives in Deformation Quantization
• Koszul duality of operads and homology of partition posets
• Homotopy algebras inspired by classical open-closed string field theory
• Cohomology and Deformation of Leibniz Pairs
• Open-closed homotopy algebra in mathematical physics
• Two-colored noncommutative Gerstenhaber formality and infinity Duflo isomorphism
• OCHA and the swiss-cheese operad
• Formality theorem for Hochschild cochains via transfer

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• Configuration Spaces of Manifolds with Boundary
• Relative Recognition Principle
• Non-formality of Voronov's Swiss-Cheese operads