On the Spectral Sequence of the Swiss-cheese Operad

Abstract

We prove that the homology of the Swiss-cheese operad is a Koszul operad. As a consequence, we obtain that the spectral sequence associated to the stratification of the compactification of points on the upper half plane collapses at the second stage, proving a conjecture by A. Voronov. However, we prove that the operad obtained at the second stage differs from the homology of the Swiss-cheese operad.

14 pages, 1 figure

References in corpus (3)

• OCHA and Leibniz Pairs, towards a Koszul duality
• Homotopy algebra of open-closed strings
• Formality theorem for Hochschild cochains via transfer

Cited by in corpus (3)

• Non-formality of the Swiss-Cheese operad
• Moduli problems for operadic algebras
• Formality of a higher-codimensional Swiss-Cheese operad