On the vector field problem for product manifolds
type: Item
instance of: scholarly article
title: On the vector field problem for product manifolds
zbMATH Open document ID: 0917.57020
author: Bernard Junod
author: Ueli Suter
published in: Hiroshima Mathematical Journal
publication date: 1999-02-17T00:00:00Z
review text: \(\text{Span}(M)\) denotes the maximal number of everywhere linearly independent tangent vector fields on a smooth compact manifold \(M\). Using K-theory methods the authors prove a criterion which gives an upper bound for \(\text{Span}(M)\), when \(M\) is a product of two stably complex manifolds. The criterion is applied to the product of lens spaces \(L^{n_1}(2^{m_1}) \times L^{n_2}(2^{m_2})\) and to the product \(N^{n_1}(m_1) \times N^{n_2}(m_2)\) of quaternionic spherical space forms, when the numbers \(m_1\) and \(m_2\) are large enough, and it is applied to products of Dold manifolds. In the case of lens spaces these upper bounds are equal to Span by a result of \textit{J. C. Becker} [Am. J. Math. 94, 991-1026 (1972; Zbl 0258.57005)].
reviewed by: K. H. Mayer
Mathematics Subject Classification ID: 57R25
Mathematics Subject Classification ID: 55N15
zbMATH DE Number: 1251458
zbMATH Keywords: geometric dimension
zbMATH Keywords: vector fields
zbMATH Keywords: K-theory
zbMATH Keywords: stably complex manifolds
zbMATH Keywords: lens spaces
zbMATH Keywords: quaternionic spherical space forms
zbMATH Keywords: Dold manifolds
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1206126676
OpenAlex ID: W2163094320
DOI: 10.32917/HMJ/1206126676
description: scientific article; zbMATH DE number 1251458