The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.
Vector Fields on the n -Sphere
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Proceedings of the National Academy of Sciences (PNAS), a peer reviewed journal of the National Academy of Sciences (NAS) - an authoritative source of high-impact, original research that broadly spans the biological, physical, and social sciences.
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“the reason for this is that most of the existing results are obtained for groups acting transitively on spheres, by fibre space relations [29; 30; 126; 133; 134; 136; 116].”
From Topology of Lie groups (1952) · cites this paper as [126]
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Citations
Cites
Products of Cocycles and Extensions of Mappings
Steenrod, N. E. (1947) · Annals of Mathematics · doi:10.2307/1969172 · Cited by 319
Self-citationEin toplogischer Beitrag zur reellen Algebra
Hopf, H. (1940) · Commentarii Mathematici Helvetici · doi:10.1007/bf01378062 · Cited by 108
Über die Abbildungen von Sphären auf Sphären niedrigerer Dimension
Hopf, H. (1964) · Springer eBooks · doi:10.1007/978-3-662-25046-4_7 · Cited by 103
�ber Richtungsfelder in den projektiven R�umen und einen Satz aus der reellen Algebra
Stiefel, E. L. (1940) · Commentarii Mathematici Helvetici · doi:10.1007/bf01378061 · Cited by 48
Systeme von Richtungsfeldern in Sphären und stetige Lösungen komplexer linearer Gleichungen
Eckmann, B. (1942) · Commentarii Mathematici Helvetici · doi:10.1007/bf02565628 · Cited by 41
Homotopy Properties of the Real Orthogonal Groups
Whitehead, G. W. (1942) · Annals of Mathematics · doi:10.2307/1968885 · Cited by 39
The (n + 2) nd Homotopy Group of the n-Sphere
Whitehead, G. W. (1950) · Annals of Mathematics · doi:10.2307/1969466 · Cited by 33
On Families of Continuous Vector Fields Over Spheres
Whitehead, G. W. (1946) · Annals of Mathematics · doi:10.2307/1969235 · Cited by 12
Correction to My Paper "On Families of Continuous Vector Fields Over Spheres"
Whitehead, G. W. (1947) · Annals of Mathematics · doi:10.2307/1969140 · Cited by 4
Flagged first, then by citations
Research works printed but not linked: 2
- 3Whitehead, G., Ibid., 47, 779-785 (1946); also 48, 782 (1947). 4 Whitehead, G., Ibid., 52, 245-247 (1950).5 Pontrjagin, L., C. R. Acad.Sci.URSS, 70, 957-959 (1950). 6 Steenrod, N., Topology of Fibre Bundles, Princeton Univ.Press, 1951, Theorems 27.16, 40.11. 7 Kirchhoff, A., C. R. Acad.Paris, 223, 1258-1260 (1948); see also reference 6, Th. 41.19.
- 13 Whitehead, J. H. C., Proc.London Math.Soc., 48, 243-291 (1944). 14 Stiefel, E., Comm.Math.Helv., 13, 201-218 (1941).15 Hopf, H., Ibid., 13, 219-239 (1941).
Cited by
Sorted by citations
Quelques propriétés globales des variétés différentiables
Thom, R. (1954) · Commentarii Mathematici Helvetici · doi:10.1007/bf02566923 · Cited by 839
Samelson, H. (1952) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1952-09544-6 · Cited by 219
“Whitehead [119] have shown, with the help of new homology invariants, that at most the spheres of dimension 2— 1”
BackgroundThe Iteration of the Steenrod Squares in Algebraic Topology
Adem, J. (1952) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.38.8.720 · Cited by 168
NON-PARALLELIZABILITY OF THE n-SPHERE FOR n > 7
Kervaire, M. A. (1958) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.44.3.280 · Cited by 138
Thomas, E. (1969) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1969-12240-8 · Cited by 121
Metadata
- Authors
- Steenrod, N. E., & Whitehead, J. H. C.
- Affiliations
- Princeton University (US)
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 1951-01
- Volume
- 37
- Issue
- 1
- Pages
- 58-63
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC1063301
- OpenAlex
- W2093117240
- Semantic Scholar
- 234df2692eadcf132a597dcff4efada98be78f46
- Cited by
- 36
- References
- 9
- Citations by year
- 2019: 1 · 2017: 1 · 2012: 1
- FWCI
- 9.82
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Geometry Research
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Equations and Dynamical Systems
- Keywords
- vector fields, n-sphere, Poincaré-Hopf theorem, Euler characteristic, topology of manifolds
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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