Algebraic vector bundles on spheres

被引：29

作者：

Asok, Aravind ^{[1
]}

Fasel, Jean ^{[2
]}

机构：

[1] Univ So Calif, Dept Math, Los Angeles, CA 90089 USA

[2] Univ Duisburg Essen, Fak Math, D-45127 Essen, Germany

来源：

JOURNAL OF TOPOLOGY | 2014年 / 7卷 / 03期

基金：

美国国家科学基金会; 瑞士国家科学基金会;

关键词：

PROJECTIVE-MODULES;

D O I：

10.1112/jtopol/jtt046

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We determine the first non-stable A(1)-homotopy sheaf of SLn. Using techniques of obstruction theory involving the A(1)-Postnikov tower, supported by some ideas from the theory of unimodular rows, we classify vector bundles of rank at least d - 1 on split smooth affine quadrics of dimension 2d - 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 of A(1) - homotopy sheaves with real and complex realization.

引用

页码：894 / 926

页数：33

共 32 条

[1]

[Anonymous], 1981, Algebraic topology

[2]

[Anonymous], 1960, Illinois J. Math.

[3]

ASOK A., 2013, PREPRINT

[4]

Asok A., 2012, PREPRINT