Vector bundles on real affine varieties
type: Item
instance of: scholarly article
title: Vector bundles on real affine varieties
zbMATH Open document ID: 0908.14004
DOI: 10.1007/BF02844511
publication date: 1997-12-17T00:00:00Z
review text: The authors consider strongly algebraic vector bundles on a real algebraic variety, i.e. projective modules over the ring of regular functions on the given variety. The main results are: (1) all vector bundles of the complement in \({\mathbb R}^3\) to an algebraic surface which has no compact connected components are trivial, (2) vector bundles on the \(n\)-dimensional sphere, where \(n<11\), have trivial restriction to \({\mathbb R}^n\). For reader's fun various parts of the article are written in English, German, French and Italian.
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14P05
zbMATH DE Number: 1089783
zbMATH Keywords: real algebraic varieties
zbMATH Keywords: vector bundles
zbMATH Keywords: projective modules
author: Friedrich Ischebeck
author: Manuel Ojanguren
reviewed by: Eugenii I. Shustin
MaRDI profile type: Publication
cites work: Analytic isomorphism and category of finitely generated modules
cites work: Q3472219
cites work: Groupes de Lie et Puissances Reduites de Steenrod
cites work: Some theorems on azumaya algebras
cites work: A Simple Proof of Gabber's Theorem on Projective Modules over a Localized Local Ring
cites work: Compositional Methods in Homotopy Groups of Spheres. (AM-49)
full work available at URL: https://doi.org/10.1007/bf02844511
OpenAlex ID: W2074422584
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 1089783