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).

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

References in corpus (1)

• Non-formality of the Swiss-Cheese operad