Algebraic vs. topological vector bundles on spheres
  We study the problem of when a topological vector bundle on a smooth complex affine variety admits an algebraic structure. We prove that all rank $2$ topological complex vector bundles on smooth affine quadrics of dimension $11$ over the complex numbers admit algebraic structures. 
Aravind Asok and Jean Fasel
math.AG math.AC math.AT math.KT