
TL;DR
This paper classifies high-rank vector bundles on certain affine quadrics using ${ m A}^1$-homotopy theory and obstruction methods, providing answers to longstanding questions about unimodular rows and vector bundle completability.
Contribution
It determines the first non-stable ${ m A}^1$-homotopy sheaf of $SL_n$ and classifies vector bundles on split smooth affine quadrics, connecting algebraic and topological perspectives.
Findings
Computed the first non-stable ${ m A}^1$-homotopy sheaf of $SL_n$
Classified vector bundles of rank ≥ d-1 on specific affine quadrics
Provided a criterion for unimodular row completability
Abstract
We determine the first non-stable -homotopy sheaf of . Using techniques of obstruction theory involving the -Postnikov tower, supported by some ideas from the theory of unimodular rows, we classify vector bundles of rank on split smooth affine quadrics of dimension . These computations allow us to answer a question posed by Nori, which gives a criterion for completability of certain unimodular rows. Furthermore, we study compatibility of our computations of -homotopy sheaves with real and complex realization.
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.
