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Journal Articles Quarterly Journal of Mathematics Year : 2024

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).
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Dates and versions

hal-04053257 , version 1 (31-03-2023)
hal-04053257 , version 2 (30-10-2023)

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Najib Idrissi, Renato Vasconcellos Vieira. Non-formality of Voronov's Swiss-Cheese operads. Quarterly Journal of Mathematics, 2024, ⟨10.1093/qmath/haad041⟩. ⟨hal-04053257v2⟩
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