Algebraic vs. topological vector bundles on spheres

Abstract

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.

13 pages; Final version before page proofs; to appear J. Ram. Math. Soc

References in corpus (2)

• A cohomological classification of vector bundles on smooth affine threefolds
• Splitting vector bundles outside the stable range and A^1-homotopy sheaves of punctured affine spaces

Cited by in corpus (1)

• Algebraic vector bundles and $p$-local A^1-homotopy theory