Enumerating complex rank $n$ vector bundles on $\mathbb CP^{n+1}$
Algebraic Topology
2026-03-03 v2
Abstract
We enumerate complex rank topological vector bundles on with prescribed Chern classes. This extends work of Atiyah and Rees in the case 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!