  Affine space over the complex numbers is simply connected in the sense that
it does not afford any non-trivial \'etale finite covers. In this paper we
prove the non-commutative analogue of this statement: an endomorphism of a Weyl
algebra provides a natural holonomic bimodule structure on the Weyl algebra. If
this bimodule is finitely generated from the left or right, then the
endomorphism is an automorphism. Finite generation of this bimodule in large
positive characteristics is equivalent to the Dixmier conjecture.

Algebraic Geometry;Rings and Algebras