On modules over valuations

Details On modules over valuations On modules over valuations

2011-02-07

arxiv.org/abs/1102.1241v2

Mathematics

Metric Geometry

11 pages; minor corrections

Scientific paper

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 $K^0$-ring constructed out of vector bundles.

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