In the construction of such homotopy commutative structures, we generally have to deal with operads which are just weakly-equivalent to the little n-discs, and the name of an E_n-operad has been introduced to refer to this notion. In this first lecture, I will give an introduction to E_n-operads and their applications. I will notably report on the following significant issues: formality, Koszul duality, and recognition theorems.
General reference:B. Fresse, "Homotopy of operads and Grothendieck-Teichmüller Groups". Book project. First volume available on the web-page "http://math.univ-lille1.fr/%7Efresse/OperadGT-December2012Preprint.pdf"
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.