Bruhat operads

Higher Bruhat orders have been introduced in our paper with Manin around 1986. They generalize the weak Bruhat orders on the symmetric groups.

In this talk, which presents a joint work with Gleb Koshevoy, I will sketch a construction which allows to build some planar operads from higher Bruhat orders. Furthermore I will explain that these operads are operads with multiplication in the sense of McClure - Smith. This implies that they give rise to some complexes having all formal properties of the Hochschild complex for an associative algebra.