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State sums, mapping classes and bracket deformation
Geometry/Topology| Speaker: | Uwe Kaiser, Boise State University |
| Location: | 2112 MSB |
| Start time: | Wed, May 17 2006, 4:10PM |
Description
The Kauffman bracket algebra of an oriented surface is
a free module with basis the isotopy classes of systems of disjoint essential
curves on the surface. It is known that the natural multiplication
of the algebra deforms the commutative product of the SL(2,C)-characters
of the fundamental group of the surface. Moreover the mapping class
group acts on the bracket algebra in a natural way.
The module isomorphism is given by the usual Kauffman state sum.
I will describe a formula, which expands this state sum in terms
of a natural algebra of diagram resolutions according to the
order of deformation. This allows to prove some new results about
the nature of the deformation.
Moreover I will give some background and examples for the problem
of explicit calculation of the product of two essential curves in the
bracket module.
This is joint work with Nikos Apostolakis