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Introduction to E_n-operads and little discs operads (mini-course)

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If you have a question about this talk, please contact Mustapha Amrani.

Grothendieck-Teichmller Groups, Deformation and Operads

The little n-discs operads, where n = 1,2,...,infinity, are used to define a hierarchy of homotopy commutative structures, from fully associative but non-commutative (n=1) up to fully associative and commutative (n=infinity).

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-Teichmller Groups”. Book project. First volume available on the web-page “http://math.univ-lille1.fr/%7Efresse/OperadGT-December2012Preprint.pdf”

This talk is part of the Isaac Newton Institute Seminar Series series.

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