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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:Homological representations for families of groups
- Arthur SouliĆ©\, Cambridge
DTSTART;TZID=Europe/London:20191113T160000
DTEND;TZID=Europe/London:20191113T170000
UID:TALK128995AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/128995
DESCRIPTION:Braid groups have a representation theory of wild
type\, in the sense that there is no known classif
ication schema. Hence it is useful to shape constr
uctions of linear representations for such family
of groups to understand its representation theory.
For this purpose\,\nLawrence and Bigelow construc
ted representations of the braid group on n strand
s using the configuration space of m points of a n
-punctured disc: namely\, the braid group acts on
the m-th homology group of a particular covering o
f the configuration space. There is actually an un
derlying general method to build such homological
representations.\n\nIn this talk\, I will present
a unified functorial approach to this method for g
eneral families of groups. I will also show that\,
under some additional assumptions\, general notio
ns of polynomiality on functors are a useful tool
to classify these representations. This is a join
t work with Martin Palmer.
LOCATION:MR13
CONTACT:Oscar Randal-Williams
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