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SUMMARY:The rational homotopy theory of operads (mini-course) - Fresse\, B
  (Universit Lille 1)
DTSTART:20130312T154500Z
DTEND:20130312T170000Z
UID:TALK43893@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The first purpose of this lecture is to explain the definition
  of an analogue of the Sullivan model for the rational homotopy of topolog
 ical operads\, and the definition of a rationalization functor on operads.
 \n\nThe Sullivan model of an operad involves both a commutative dg-algebra
  structure\, which encodes the rational homotopy type of the spaces underl
 ying the operad\, and a cooperad structure\, which models the composition 
 structure attached to our topological operad.\nIf we neglect the commutati
 ve algebra part of the structure\, then we get a model for the stable rati
 onal homotopy of operads\, and an operadic version of the Sullivan miminal
  model can also be defined in this setting. But the construction of minima
 l models fails when we deal with the combination of commutative algebra an
 d operad structures involved in our model for the rational homotopy of ope
 rads in topological spaces. So does the definition of the Quillen model\, 
 as well as the classical approach to integrate deformation complexes into 
 rational homotopy automorphism groups.\n\nI will explain methods to bypass
  these difficulties\, and which can be used to establish the main result o
 f this lecture series in the little 2-discs case.\n\nGeneral reference:B. 
 Fresse\, "Homotopy of operads and Grothendieck-Teichmller Groups".  Book p
 roject. First volume available on the web-page  "http://math.univ-lille1.f
 r/%7Efresse/OperadGT-December2012Preprint.pdf"\n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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