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The elementary algebra of K-theory

Part of the Oberwolfach Seminars book series (OWS, volume 36)

Abstract

Originally, K-theory was the study of vector bundles on topological spaces. But it was soon realised that the notion of vector bundle can be formulated more algebraically: Swan’s Theorem identifies the monoid of vector bundles over a compact space X with the monoid of finitely generated projective modules over the algebra C(X) of continuous functions on X; we take real- or complex-valued functions here to get real or complex vector bundles, respectively.

Keywords

Abelian Group Vector Bundle Euler Characteristic Projective Module Invertible Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag AG 2007

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