2020/09/21 by Andrew D. Lewis, Lewis, Andrew D.
Mathematics · #32C05 #32C09 #32C22 #32C35 #32L10 #32Q40 #58A07 #58A20 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2009.09757
openalex publication_date 2020/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In general terms, Gelfand duality refers to a correspondence between a geometric, topological, or analytical category, and an algebraic category. For example, in smooth differential geometry, Gelfand duality refers to the topological embedding of a smooth manifold in the topological dual of its algebra of smooth functions. This is generalised here in two directions. First, the topological embeddings for manifolds are generalised to the cases of real analytic and Stein manifolds, using a unified cohomological argument. Second, this type of duality is extended to vector bundles, affine bundles, and jet bundles by using suitable classes of functions, the topological duals in which the embeddings take their values.