Serre-Swan theorem

Let X be a compactPlanetmathPlanetmath Hausdorff space. Let 𝐕𝐞𝐜(X) be the categoryMathworldPlanetmath of complex vector bundles over X. And, let 𝐏𝐫𝐨𝐣𝐌𝐨𝐝(C(X)) be the category of finitely generated projective modules over the C*-algebraPlanetmathPlanetmath C(X). There is a functorMathworldPlanetmath Γ:𝐕𝐞𝐜(X)𝐏𝐫𝐨𝐣𝐌𝐨𝐝(C(X)) which sends each complex vector bundle EX to the C(X)-module Γ(X,E) of continuous sections.

The functor Γ is an equivalence of categories.

Title Serre-Swan theorem
Canonical name SerreSwanTheorem
Date of creation 2013-03-22 13:29:31
Last modified on 2013-03-22 13:29:31
Owner mhale (572)
Last modified by mhale (572)
Numerical id 5
Author mhale (572)
Entry type Theorem
Classification msc 46L85