Topology seminar @ Università degli studi di Roma "Tor Vergata"

Operads are algebraic structures capturing multi-ary operations. The little disks operads, encoding operations on iterated loop spaces, are fundamental examples. Voronov introduced Swiss-Cheese operads, which generalize little disks to relative loop spaces of pairs of spaces. While the little disks operads are formal (their cohomology determines their rational homotopy type), the standard Swiss-Cheese operads are not. We will discuss why higher-codimensional Swiss-Cheese operads are formal, and why Voronov’s original version is not. This non-formality result, stemming from joint work with R. V. Vieira, leads to questions about truncations and Massey products.