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SUMMARY:Homotopy automorphisms of operads in topological spaces (mini-cour
 se) - Fresse\, B (Universit Lille 1)
DTSTART:20130305T154500Z
DTEND:20130305T170000Z
UID:TALK43818@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The Grothendieck-Teichmller group can be defined algebraically
 \, as the automorphism group of an operad in groupoids\, the operad of par
 enthesized braids. I will explain that this operad represents the fundamen
 tal groupoid of the little 2-discs operad.\nThe homotopy automorphisms con
 sidered in my lecture series represent a topological counterpart of the au
 tomorphisms of an algebraic operad. In this lecture\, I will explain the p
 recise definition of this notion\, and of a rational version of the notion
  of a homotopy automorphism\, where we neglect torsion phenomena.\n\nThe r
 esult which I aim to establish precisely asserts that\, in the case of the
  little 2-discs operad\, the group of rational homotopy automorphisms redu
 ce to homotopy automorphisms that can be detected by their action on funda
 mental groupoids.\n\nGeneral reference:B. Fresse\, "Homotopy of operads an
 d Grothendieck-Teichmller Groups".  Book project. First volume available o
 n the web-page  "http://math.univ-lille1.fr/%7Efresse/OperadGT-December201
 2Preprint.pdf"\n\n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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