Enumerating complex rank $n$ vector bundles on $\mathbb CP^{n+1}$

TL;DR

This paper classifies complex rank n vector bundles on complex projective spaces with given Chern classes, extending previous classifications for specific cases.

Contribution

It generalizes the enumeration of complex rank n vector bundles on  ext{CP}^{n+1} for arbitrary Chern classes, building on prior special cases.

Findings

Complete enumeration of bundles with prescribed Chern classes

Extension of Atiyah-Rees classification to higher n

Results applicable to topological vector bundle theory

Abstract

We enumerate complex rank $n$ topological vector bundles on $\mathbb CP^{n+1}$ with prescribed Chern classes. This extends work of Atiyah and Rees in the case $n=2$ and work of Hu in the case that all Chern classes are zero.