The following paper and its references contains  some  algebraic consequences of  vector bundle theory.

>Vakhtang Lomadze, _Applications of vector bundles to factorization of rational matrices_, Linear Algebra and its Applications **288** (1999) pp249–258, doi:[10.1016/S0024-3795(98)10220-3][1]

[1]: http://dx.doi.org/10.1016/S0024-3795%2898%2910220-3