2021/01/04 by Mehdi Nabil, Nabil, Mehdi
Mathematics · #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2101.00946
openalex publication_date 2021/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a smooth manifold. When Γ is a group acting on the manifold M by diffeomorphisms one can define the Γ-co-invariant cohomology of M to be the cohomology of the differential complex Ωc(M)Γ=span\ω-γ^*ω, ω∈Ωc(M), γ∈Γ\. For a Lie algebra G acting on the manifold M, one defines the cohomology of G-divergence forms to be the cohomology of the complex CG(M)=span\LXω, ω∈Ωc(M), X\inG\. In this short paper we present a situation where these two cohomologies are infinite dimensional.