Algebraic vs. topological vector bundles on spheres

TL;DR

This paper investigates the conditions under which topological vector bundles on smooth complex affine varieties can be given algebraic structures, proving that all rank 2 bundles on certain 11-dimensional quadrics are algebraic.

Contribution

It establishes that all rank 2 topological complex vector bundles on smooth affine quadrics of dimension 11 admit algebraic structures, advancing understanding of vector bundle classification.

Findings

All rank 2 topological bundles on 11-dimensional smooth affine quadrics are algebraic.

Provides conditions for when topological bundles admit algebraic structures.

Enhances the connection between topological and algebraic vector bundles on complex varieties.

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.