Non-formality of Voronov's Swiss-Cheese operads

Najib Idrissi, Renato Vasconcellos Vieira
Preprint v1, 29 pages.
Online on


The Swiss-Cheese operads, which encode actions of algebras over the little nn-cubes operad on algebras over the little (n1)(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 (2,2n)(2,2^n), rather than (2,0)(2,0) (Livernet) or (4,0)(4,0) (Willwacher).