@inbook{b277379d91c247209b8fae54e2160388,
title = "On modules over valuations",
abstract = "To any smooth manifold X an algebra of smooth valuations V ∞ (X) was associated in [Alesker, Israel J. Math. 156, 311-339 (2006); Adv. Math. 207(1), 420-454 (2006); Theory of Valuations on Manifolds, IV. New Properties of the Multiplicative Structure (2007); Alesker, Fu, Trans. Am. Math. Soc. 360(4), 1951-1981 (2008)]. In this note we initiate a study of V ∞ (X)-modules. 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 for a compact manifold X there exists a canonical isomorphism between the K-ring constructed out of finitely generated projective V ∞ (X)-modules and the classical topological K 0-ring constructed out of vector bundles over X.",
author = "Semyon Alesker",
note = "Funding Information: I thank M. Borovoi for useful discussions on non-abelian cohomology, and F. Schuster for numerous remarks on the first version of the paper. Partially supported by ISF grant 701/08.",
year = "2012",
doi = "10.1007/978-3-642-29849-3_2",
language = "الإنجليزيّة",
isbn = "9783642298486",
series = "Lecture Notes in Mathematics",
publisher = "Springer Verlag",
pages = "23--34",
booktitle = "Geometric Aspects of Functional Analysis",
address = "ألمانيا",
}