Operads & Grothendieck-Teichmüller groups - draft document

Benoit Fresse (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

This preprint is an extract from a research monograph, currently 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 Grothendieck-Teichmüller 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 draft document 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.

Mots clés: Operads; Rational homotopy theory; Grothendieck-Teichmüller groups; Braid groups; En-operads; Homotopical algebra.; Homotopical algebra

Domaines: Topologie algébrique [math.AT]

Benoit Fresse. Operads & Grothendieck-Teichmüller groups - draft document. 2012. ⟨hal-00656333⟩