2011/02/07 by Semyon Alesker, Alesker, Semyon
Mathematics · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Metric Geometry (math.MG) #math.KT #math.MG
paper · pdf · doi:10.48550/arxiv.1102.1241
11 pages; minor corrections
openalex publication_date 2011/02/07 · arxiv created 2011/04/05 · arxiv updated 2011/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently an algebra of smooth valuations was attached to any smooth manifold. Roughly put, a smooth valuation is finitely additive measure on compact submanifolds with corners which satisfies some extra properties. In this note we initiate a study of modules over smooth valuations. More specifically we study finitely generated projective modules in analogy to the study of vector bundles on a manifold. In particular it is shown that on a compact manifold there exists a canonical isomorphism between the K-ring constructed out of finitely generated projective modules over valuations and the classical topological K0-ring constructed out of vector bundles.