Self-maps of sphere bundles. II
type: Item
instance of: scholarly article
title: Self-maps of sphere bundles. II
zbMATH Open document ID: 0695.55009
author: J. Lyle Noakes
published in: Kodai Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: Let \(S^ q\to E\to S^{r+1}\) be an oriented orthogonal q-sphere bundle. A fibre preserving map f: \(E\to E\) induces the degree m say on the fibre. In an earlier paper [J. Pure Appl. Algebra 10, 95-99 (1977; Zbl 0367.55017)] the author gave results on the structure, for more general base-space, of the set A(E) of integers m for which there is a fibre preserving map of degree m. In the case where q is odd, homotopical obstructions are given here to the existence of a map of degree m: in the case where \(q=1\), 3 or 7 these conditions become necessary and sufficient. In the case where q is even and the bundle has a cross section, necessary and sufficient homotopical conditions for the existence of a map of degree m are given: in particular there are in this case fibre preserving maps of all odd degrees and all degrees \(m\equiv 0 mod 4\).
Mathematics Subject Classification ID: 55Q05
Mathematics Subject Classification ID: 55R10
zbMATH DE Number: 4138774
zbMATH Keywords: orthogonal sphere bundle
zbMATH Keywords: fibre preserving map
zbMATH Keywords: degree
zbMATH Keywords: obstructions
zbMATH Keywords: cross section
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138038935
OpenAlex ID: W2034362809
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DOI: 10.2996/KMJ/1138038935
description: scientific article; zbMATH DE number 4138774