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

Title
(Non-)formality of Swiss-Cheese operads and variants
Event
Colloque 2021 du GDR Topologie Algébrique et Applications
Location
Université de Strasbourg
On

## Abstract

The usual Swiss-Cheese operad encodes triplets , where is an algebra over the little disks operad in dimension (i.e., an algebra), is an -algebra, and is a central morphism of -algebras. The Swiss-Cheese operad admits several variants and generalizations. In Voronov’s original version, the morphism is replaced by an action ; in the extended Swiss-Cheese operad , the lower algebra is an -algebra for some ; and in the complementarily-constrained disks operad , the morphism is replaced by a derivation . 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.