  The objective of this paper is the proof of a conjecture of Kontsevich on the
isomorphism between groups of polynomial symplectomorphisms and automorphisms
of the corresponding Weyl algebra in characteristic zero. The proof is based on
the study of topological properties of automorphism $\Ind$-varieties of the
so-called augmented and skew augmented versions of Poisson and Weyl algebras.
Approximation by tame automorphisms as well as a certain singularity analysis
procedure is utilized in the construction of the lifting of augmented
polynomial symplectomorphisms, after which specialization of the augmentation
parameter is performed in order to obtain the main result.
