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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:Rational homotopy theory of the little n-disks ope
rads - Thomas Willwacher\, Zurich
DTSTART;TZID=Europe/London:20160210T160000
DTEND;TZID=Europe/London:20160210T170000
UID:TALK62442AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/62442
DESCRIPTION:The little n-disks operads are classical objects i
n topology\, introduced by Boardman-Vogt and May i
n the 1970's in their study of iterated loop space
s. They have since seen a wealth of applications i
n algebra and topology\, and received much attenti
on recently due to their appearance in the manifol
d calculus of Goodwillie and Weiss\, and relatedly
in the factorization (or topological chiral) homo
logy by Lurie\, Francis\, Beilinson-Drinfeld and o
thers. \nI report on recent joint work with V. Tur
chin and Benoit Fresse\, in which we (mostly) sett
le the rational homotopy theory of the little n-di
sks operads\, by showing that they are intrinsical
ly formal for n>=3\, and by computing the rational
homotopy type of the function spaces between thes
e objects in terms of combinatorial graph complexe
s. As an application we obtain complete rational c
ombinatorial invariants of long knots in codimensi
on >=3.
LOCATION:MR13
CONTACT:Ivan Smith
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