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SUMMARY:Rational homotopy theory of the little n-disks operads - Thomas Wi
 llwacher\, Zurich
DTSTART:20160210T160000Z
DTEND:20160210T170000Z
UID:TALK62442@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:The little n-disks operads are classical objects in topology\,
  introduced by Boardman-Vogt and May in the 1970's in their study of itera
 ted loop spaces. They have since seen a wealth of applications in algebra 
 and topology\, and received much attention recently due to their appearanc
 e in the manifold calculus of Goodwillie and Weiss\, and relatedly in the 
 factorization (or topological chiral) homology by Lurie\, Francis\, Beilin
 son-Drinfeld and others. \nI report on recent joint work with V. Turchin a
 nd Benoit Fresse\, in which we (mostly) settle the rational homotopy theor
 y of the little n-disks operads\, by showing that they are intrinsically f
 ormal for n>=3\, and by computing the rational homotopy type of the functi
 on spaces between these objects in terms of combinatorial graph complexes.
  As an application we obtain complete rational combinatorial invariants of
  long knots in codimension >=3.
LOCATION:MR13
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