On deformation theory and graph homology
  Deformation theory of associative algebras and in particular of Poisson algebras is reviewed. The role of an almost contraction leading to a canonical solution of the corresponding Maurer-Cartan equation is noted. This role is reminiscent of the homotopical perturbation lemma, with the infinitesimal deformation cocycle as initiator.   Applied to star-products, we show how Moyal's formula can be obtained using such an almost contraction and conjecture that the merger operation provides a canonical solution at least in the case of linear Poisson structures. 
Fusun Akman (1), Lucian M. Ionescu (1), Papa A. Sissokho (1) ((1)   Illinois State University)