2004/06/08 by Toby N. Bailey, Toby Bailey, Michael Eastwood +4
Mathematics · #32L25 #43A85 #Advanced Combinatorial Mathematics #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Primary 32L10 #Secondary 22E46 #math.CV #msc:22E46 #msc:32L10 #msc:32L25 #msc:43A85
paper · pdf · doi:10.48550/arxiv.math/0406142
15 pages
arxiv created 2004/06/08 · openalex publication_date 2004/06/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Stein covering of a complex manifold may be used to realise its analytic cohomology in accordance with the Cech theory. If, however, the Stein covering is parameterised by a smooth manifold rather than just a discrete set, then we construct a cohomology theory in which an exterior derivative replaces the usual combinatorial Cech differential. Our construction is motivated by integral geometry and the representation theory of Lie groups.