Serre-Swan theorem
Let be a compact Hausdorff space.
Let be the category
of complex vector bundles over .
And, let be the category of finitely generated projective modules over the -algebra
.
There is a functor
which sends each complex vector bundle to the -module of continuous sections.
The functor 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 |