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 [Contemp. Math. 239 (1999) 365–373]. However, we prove that the operad obtained at the second stage differs from the homology of the Swiss-cheese operad.