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We derive a formula expanding the bracket with respect to a natural deformation parameter. The expansion is in terms of a two-variable polynomial algebra of diagram resolutions generated by basic operations involving the Goldman bracket. A functorial characterization of this algebra is given. Differentiability properties of the star product underlying the Kauffman bracket are discussed.
The aim of this short communication is to review some classical results on string topology of manifolds and discuss recent extensions of this theory to orbifolds. In particular, we review the relation between the loop homology of the classiying space of the orbifold and the Hochschild cohomology of dg-ring naturally associated to the orbifold.