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Colloque 2021 du GDR Topologie Algébrique et Applications @ Université de Strasbourg

On . Title: (Non-)formality of Swiss-Cheese operads and variants.

The usual Swiss-Cheese operad encodes triplets (A,B,f)(A,B,f), where AA is an algebra over the little disks operad in dimension nn (i.e., an En\mathsf{E}_n algebra), BB is an En1\mathsf{E}_{n-1}-algebra, and f:AZ(B)f : A \to Z(B) is a central morphism of EnE_n-algebras. The Swiss-Cheese operad admits several variants and generalizations. In Voronov’s original version, the morphism is replaced by an action ABBA \otimes B \to B; in the extended Swiss-Cheese operad ESCmn\mathsf{ESC}_{mn}, the lower algebra is an Em\mathsf{E}_m-algebra for some m<nm < n; and in the complementarily-constrained disks operad CDmn\mathsf{CD}_{mn}, the morphism is replaced by a derivation f+ϵδ:AB[ϵ]f + \epsilon \delta : A \to B[\epsilon]. In this talk, I will explain approaches to prove the (non-)formality of some of the variants of the Swiss-Cheese operad, including a joint work in progress with Renato Vasconcellos Vieira.

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