Projective modules over the real algebraic sphere of dimension 3

TL;DR

This paper proves that every projective module over the coordinate ring of the 3-dimensional real algebraic sphere is free, confirming a specific case of algebraic vector bundle triviality.

Contribution

It establishes that all projective modules over the coordinate ring of the 3D real algebraic sphere are free, a significant result in algebraic geometry.

Findings

All projective modules over the coordinate ring are free.

Supports the conjecture on algebraic vector bundles over spheres.

Advances understanding of algebraic structures on real algebraic spheres.

Abstract

We show that all the projective modules over the coordinate ring of the real algebraic sphere of dimension 3 are free