Nonlinear Spencer operators on differentiable groupoids

Abstract

We construct the first, second and sophisticated non-linear and linear Spencer complexes for a differentiable Lie groupoid $G$. To do this, we extend the diagonal calculus, as applied by Malgrange to the groupoid $M\times M$, to the context of $I\times G$, where $I$ is the manifold of identities of $G$.