OPERADS & GROTHENDIECK - TEICHMÜLLER GROUPS – DRAFT DOCUMENT by

This preprint is an extract from a research monograph in preparation on the homotopy of operads and Grothendieck-Teichmüller groups. The ultimate objective of this book is to prove that the Grothendieck-Teichmüller group is the group of homotopy automorphisms of a rational completion of the little 2-discs operad. The present excerpts include a comprehensive account of the fundamental concepts of operad theory, a survey chapter on little discs operads as well as a detailed account on the connections between little 2-discs, braid groups, and GrothendieckTeichmüller groups, until the formulation of the main result of the monograph. Most concepts are carefully reviewed in order to make this account accessible to a broad readership, which should include graduate students as well as researchers coming from the various fields of mathematics related to our main topics. This preprint will serve as reference material for a master degree course “Operads 2012”, given by the author at université Lille 1, from January until April 2012. See: http://math.univ-lille1.fr/~operads/2012courses.html#Lille This working draft will not be updated, and the given excerpts should significantly differ from the final version of the monograph in preparation. Nevertheless, a copy with annotated corrections will be made available on the above web-page. This work has mostly been written during stays at the École Normale Supérieure de Paris, at Northwestern University, and at the Max-Planck-Institut für Mathematik in Bonn. The author is grateful to these institutions for outstanding working conditions, and to numerous colleagues for their warm welcome which has greatly eased this writing task.