Poincaré's lemma for formal manifolds

Abstract

This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In two previous papers, we develop the basic theory of formal manifolds, including generalizations of vector-valued distributions and generalized functions on smooth manifolds to the setting of formal manifolds. In this paper, we establish Poincaré's lemma for de Rham complexes with coefficients in formal functions, formal generalized functions, compactly supported formal densities, or compactly supported formal distributions.

The preprint arXiv:2401.01535v1 of ours was split into three separate papers. This is the third paper about de Rham complexes and Poincare's Lemma