English

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

Algebraic Topology 2026-03-03 v2

Abstract

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

Keywords

Cite

@article{arxiv.2410.23520,
  title  = {Enumerating complex rank $n$ vector bundles on $\mathbb CP^{n+1}$},
  author = {Morgan P. Opie},
  journal= {arXiv preprint arXiv:2410.23520},
  year   = {2026}
}

Comments

Updated with corrected proof of Theorem 4.3, plus some minor typos fixed. 13 pages, comments welcome!

R2 v1 2026-06-28T19:42:12.663Z