In the mathematical fields of differential geometry, topology and algebraic geometry, the Serre–Swan theorem, also called Swan's theorem, relates the geometric notion of vector bundles to the algebraic concept of projective modules and gives rise to a common intuition throughout mathematics: "projective modules are like vector bundles". The three precise formulations of the theorem differ somewhat.
In the mathematical fields of differential geometry, topology and algebraic geometry, the Serre–Swan theorem, also called Swan's theorem, relates the geometric notion of vector bundles to the algebraic concept of projective modules and gives rise to a common intuition throughout mathematics: "projective modules are like vector bundles". The three precise formulations of the theorem differ somewhat.
Source: Wikipedia "Serre–Swan theorem" · CC BY-SA 4.0
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