Algebraic vector bundles on spheres. (3rd February 2014)

• Record Type: Journal Article
• Authors: Asok, Aravind; Fasel, Jean
• Is Part Of: Journal of topology. Volume 7:Part 3(2014)
• Page Start: 894
• Page End: 926
• Publication Date: 2014-02-03
• Subjects: Topology -- Periodicals; 514.05
• DOI: 10.1112/jtopol/jtt046
• Languages: English
• ISSNs: 1753-8416

Abstract

Abstract : We determine the first non‐stableA 1 ‐homotopy sheaf ofSL n . Using techniques of obstruction theory involving theA 1 ‐Postnikov tower, supported by some ideas from the theory of unimodular rows, we classify vector bundles of rank at leastd ‐ 1 on split smooth affine quadrics of dimension2 d ‐ 1 . 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 ofA 1 ‐homotopy sheaves with real and complex realization.