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

http://www.sciencedirect.com/science/article/pii/S0024379598102203

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