Non-formality of Voronov's Swiss-Cheese operads

Abstract

The Swiss-Cheese operads, which encode actions of algebras over the little $n$-cubes operad on algebras over the little $(n-1)$-cubes operad, comes in several variants. We prove that the variant in which open operations must have at least one open input is not formal in characteristic zero. This is slightly stronger than earlier results of Livernet and Willwacher. The obstruction to formality that we find lies in arity $(2,2^n)$, rather than $(2,0)$ (Livernet) or $(4,0)$ (Willwacher).

arXiv commentThe Mathematica code for the figures is going to appear alongside the article in the HAL preprint server

References in corpus (9)

• Deformation quantization of Poisson manifolds, I
• Operads and Motives in Deformation Quantization
• Equivalences of monoidal model categories
• The Homotopy Braces Formality Morphism
• OCHA and Leibniz Pairs, towards a Koszul duality
• Non-formality of the Swiss-Cheese operad
• (Non-)formality of the extended Swiss Cheese operads
• On the formality of the little disks operad in positive characteristic
• Swiss-Cheese operad and Drinfeld center