Join products and indices of \(k\)-fields over differentiable fiber bundles.
type: Item
instance of: scholarly article
title: Join products and indices of \(k\)-fields over differentiable fiber bundles.
zbMATH Open document ID: 1058.57020
author: Nancy de Souza Cardim
author: Maria Hermínia de P. L. Mello
author: Mário Olivero Marques da Silva
author: Duane Randall
published in: Topology and its Applications
publication date: 2004-02-03T00:00:00Z
review text: The intrinsic join product is used to study indices of \(k\)-fields with finite singularities defined on the total space of a differentiable fibre bundle. This is expressed as the product of the indices of \(k\)-fields with finite singularities given on the fiber and the base. The computations of the join product of the generators of \(\pi_{n-1}(V_{n,k})\) for \(1<k \leq 4\) are presented in the case of the real Stiefel manifold \(\pi_{n-1}(V_{n,k})\) of \(k\)-frames in \(\mathbb R^{n}\). The indices of k-fields with finite singularities on a smooth closed manifold \(M^{n}\) are expressed precisely in terms of generators of \(\pi_{n-1}(V_{n,k})\) for \(1<k \leq 4\) when the indices depend only on the oriented homotopy type of \(M^{n}\). Finally, direct proofs of some results of \textit{J. C. Becker} and \textit{R. E. Schultz} [Q. J. Math., Oxf. II. Ser. 33, 385--403 (1982; Zbl 0512.55015)] concerning the existence of differentiable fiber bundles are obtained.
Mathematics Subject Classification ID: 57R25
Mathematics Subject Classification ID: 55R10
Mathematics Subject Classification ID: 55Q35
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 2037259
zbMATH Keywords: fiber bundle
zbMATH Keywords: Stiefel manifold
zbMATH Keywords: k-field
zbMATH Keywords: indices
zbMATH Keywords: intrinsic join product
zbMATH Keywords: homotopy groups
reviewed by: Gheorghe Pitiş
MaRDI profile type: Publication
full work available at URL: j.topol.2003.08.008
OpenAlex ID: W2065073516
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DOI: 10.1016/J.TOPOL.2003.08.008
description: scientific article; zbMATH DE number 2037259