2024/08/08 by Fulin Chen, Chen, Fulin, Binyong Sun +3
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2408.04263
openalex publication_date 2024/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.