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SUMMARY:Braids and the Grothendieck-Teichmuller Group - Bar-Natan\, D (Uni
 versity of Toronto)
DTSTART:20130109T100000Z
DTEND:20130109T110000Z
UID:TALK42341@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:I will explain what are associators (and why are they useful a
 nd natural) and what is the Grothendieck-Teichmüller group\, and why it i
 s completely obvious that the Grothendieck-Teichmuller group acts simply t
 ransitively on the set of all associators. Not enough will be said about h
 ow this can be used to show that "every bounded-degree associator extends"
 \, that "rational associators exist"\, and that "the pentagon implies the 
 hexagon". \n<p></p>\nIn a nutshell: the filtered tower of braid groups (wi
 th bells and whistles attached) is isomorphic to its associated graded\, b
 ut the isomorphism is neither canonical nor unique - such an isomorphism i
 s precisely the thing called "an associator". But the set of isomorphisms 
 between two isomorphic objects *always* has two groups acting simply trans
 itively on it - the group of automorphisms of the first object acting on t
 he right\, and the group of automorphisms of the second object acting on t
 he left. In the case of associators\, that first group is what Drinfel'd c
 alls the Grothendieck-Teichmuller group GT\, and the second group\, isomor
 phic (though not canonically) to the first\, is the "graded version" GRT o
 f GT.  \nAll the references and material for this talk can be found there:
  http://www.math.toronto.edu/~drorbn/Talks/Newton-1301/ .
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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