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SUMMARY:Skein algebra\, 3-manifolds and categorification - Paul Wedrich (I
 mperial)
DTSTART:20170317T150000Z
DTEND:20170317T160000Z
UID:TALK69292@talks.cam.ac.uk
CONTACT:36916
DESCRIPTION:The Jones polynomial and its cousins are invariants of knots a
 nd links in the 3-sphere\, which are determined by local so-called skein r
 elations. This allows a simple definition of an invariant of oriented 3-ma
 nifolds M: the space of all framed links in M modulo the skein relations. 
 Of particular interest are these invariants for thickened surfaces\, in wh
 ich case they carry an algebra structure and act on the invariants of 3-ma
 nifolds co-bounding the surface. They are also related to character variet
 ies\, quantum Teichmueller spaces and feature in several important conject
 ures in quantum topology. After surveying this area\, I will talk about po
 sitive bases for skein algebras that were found by D. Thurston\, and how t
 hey might be related to Khovanov's categorification of the Jones polynomia
 l and its desired extension to a 4-dimensional TQFT.
LOCATION:MR13
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