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Odd Chern-Simons theory and the construction of characteristic classes
  OKC/Nordita High-Energy Physics Theory seminar

Monday 30 November 2009
from 13:30 to 14:30
at Nordita seminar room 132:028
Speaker : Jian Qiu (Uppsala University)
Abstract : The perturbation expansion of Chern-Simons theory is rich in its structure. It was shown by Kontsevich that the perturbation expansion in fact realises a pairing of two dual constructions of graph (co)homology. One of the above constructions is related to the knot invariants of the 3D manifold on which CS lives, while its dual coonstruction is related to the Lie algebra cohomology of the gauge group. Inspired by this, we constructed an analogue of Chern-Simons which is odd (in both senses). This allows us to study and construct cocycles of the Chevalley Eilenberg complex of the Lie algebra of formal Hamiltonian vector fields. After this one can apply the well known Chern-Weil construction to obtain characteristic classes of, say, Poisson manifold, Lie algebroids and foliations etc. I will give a physicists' explaination of the mathematical objects introduced above.

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