English

Metastable complex vector bundles over complex projective spaces

Algebraic Topology 2022-02-25 v1 Algebraic Geometry

Abstract

We apply Weiss calculus to compute the number of topological complex vector bundles of rank n2n-2 with vanishing Chern classes over CPn\mathbb{C}P^n for n>3n>3, as given by the list 1,1,12,2,1,3,2,2,3,1,4,6,1,1,6,2,1,3,4,2,3,1,2,61, 1, 12, 2, 1, 3, 2, 2, 3, 1, 4, 6, 1, 1, 6, 2, 1, 3, 4, 2, 3, 1, 2, 6, where the ii-th entry in this list is the number of such bundles whenever nn is congruent to ii modulo 2424, starting with i=0i = 0. Similarly, the number of rank n1n-1 bundles with vanishing Chern classes over CPn\mathbb{C}P^n for n>2n>2 is 22 when nn is odd and 11 when nn is even.

Keywords

Cite

@article{arxiv.2202.11800,
  title  = {Metastable complex vector bundles over complex projective spaces},
  author = {Yang Hu},
  journal= {arXiv preprint arXiv:2202.11800},
  year   = {2022}
}
R2 v1 2026-06-24T09:51:54.526Z