Metastable complex vector bundles over complex projective spaces
Yang Hu

TL;DR
This paper uses Weiss calculus to explicitly compute the counts of certain topological complex vector bundles with vanishing Chern classes over complex projective spaces, revealing intricate periodic patterns.
Contribution
It introduces a novel application of Weiss calculus to determine exact numbers of topological bundles over complex projective spaces, providing explicit formulas and patterns.
Findings
Number of rank n-2 bundles with vanishing Chern classes over CP^n for n>3
Number of rank n-1 bundles with vanishing Chern classes over CP^n for n>2
Identifies periodic patterns in bundle counts based on n modulo 24
Abstract
We apply Weiss calculus to compute the number of topological complex vector bundles of rank with vanishing Chern classes over for , as given by the list , where the -th entry in this list is the number of such bundles whenever is congruent to modulo , starting with . Similarly, the number of rank bundles with vanishing Chern classes over for is when is odd and when is even.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topology and Set Theory · Algebraic Geometry and Number Theory
