The elementary algebra of K-theory
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.
KeywordsAbelian Group Vector Bundle Euler Characteristic Projective Module Invertible Element
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