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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Braids and the Grothendieck-Teichmuller Group - Ba
r-Natan\, D (University of Toronto)
DTSTART;TZID=Europe/London:20130109T100000
DTEND;TZID=Europe/London:20130109T110000
UID:TALK42341AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/42341
DESCRIPTION:I will explain what are associators (and why are t
hey useful and natural) and what is the Grothendie
ck-Teichmüller group\, and why it is completely ob
vious that the Grothendieck-Teichmuller group acts
simply transitively on the set of all associators
. Not enough will be said about how this can be us
ed to show that "every bounded-degree associator e
xtends"\, that "rational associators exist"\, and
that "the pentagon implies the hexagon". \n
\nIn a nutshell: the filtered tower of braid group
s (with bells and whistles attached) is isomorphic
to its associated graded\, but the isomorphism is
neither canonical nor unique - such an isomorphis
m is precisely the thing called "an associator". B
ut the set of isomorphisms between two isomorphic
objects *always* has two groups acting simply tran
sitively on it - the group of automorphisms of the
first object acting on the right\, and the group
of automorphisms of the second object acting on th
e left. In the case of associators\, that first gr
oup is what Drinfel'd calls the Grothendieck-Teich
muller group GT\, and the second group\, isomorphi
c (though not canonically) to the first\, is the "
graded version" GRT of GT. \nAll the references a
nd material for this talk can be found there: http
://www.math.toronto.edu/~drorbn/Talks/Newton-1301/
.
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
CONTACT:Mustapha Amrani
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