Stably extendible vector bundles over the quaternionic projective spaces
type: Item
instance of: scholarly article
title: Stably extendible vector bundles over the quaternionic projective spaces
zbMATH Open document ID: 0932.55020
author: Mitsunori Imaoka
author: Kouji Kuwana
published in: Hiroshima Mathematical Journal
publication date: 1999-11-29T00:00:00Z
review text: Let \(\mathbb HP^n\) denote quaternionic projective \(n\)-space. Let a quaternionic \(k\)-dimensional \((k\leq n)\) vector bundle \(\gamma\) over \(\mathbb HP^n\) be stably extendible (that is, for each \(m\geq n\), the bundle \(\gamma\) is stably equivalent to the \(\mathbb HP^n\)-restriction of a quaternionic \(k\)-dimensional vector bundle \(\widetilde\gamma_m\) over \(\mathbb HP^m\)). Supposing that the top nonzero symplectic Pontryagin class of \(\gamma\) does not vanish mod \(2\), the authors prove that \(\gamma\) is stably equivalent to a sum of \(k\) quaternionic line bundles. They give an example showing that the Pontryagin class condition cannot be removed.
Mathematics Subject Classification ID: 55R50
Mathematics Subject Classification ID: 57R22
Mathematics Subject Classification ID: 55R40
zbMATH DE Number: 1347346
zbMATH Keywords: extendible vector bundle
zbMATH Keywords: quaternionic projective space
zbMATH Keywords: symplectic Pontryagin class
reviewed by: Július Korbaš
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1347346