Vector bundles on real affine varieties (Q1373413)

The authors consider strongly algebraic vector bundles on a real algebraic variety, i.e. projective modules over the ring of regular functions on the given variety. The main results are: (1) all vector bundles of the complement in \({\mathbb R}^3\) to an algebraic surface which has no compact connected components are trivial, (2) vector bundles on the \(n\)-dimensional sphere, where \(n<11\), have trivial restriction to \({\mathbb R}^n\). For reader's fun various parts of the article are written in English, German, French and Italian.