Higher Bruhat orders and higher 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.