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Commentary on ``On the parallelizability of the spheres'' by R. Bott and J. Milnor and ``On the nonexistence of elements of Hopf invariant one'' by J. F. Adams


Author: Andrew Ranicki
Journal: Bull. Amer. Math. Soc. 48 (2011), 509-511
MSC (2010): Primary 57R22, 17A35
DOI: https://doi.org/10.1090/S0273-0979-2011-01345-3
Published electronically: June 14, 2011
Link to article that is the subject of this commentary: Bull. Amer. Math. Soc. 64 (1958), Part 1:87--89.
Link to article that is the subject of this commentary: Bull. Amer. Math. Soc. 64 (1958), 279-282.
MathSciNet review: 2823019
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References [Enhancements On Off] (What's this?)

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  • [Ad2] J. F. Adams, On the non-existence of elements of Hopf invariant one, Ann. of Math. (2) 72 (1960), 20-104. MR 0141119 (25:4530)
  • [AdAt] J. F. Adams and M. F. Atiyah, $ K$-theory and the Hopf invariant, Quart. J. Math. Oxford (2) 17 (1966), 31-38. MR 0198460 (33:6618)
  • [BoMi] R. Bott and J. Milnor, On the parallelizability of the spheres, Bull. Amer. Math. Soc. 64 (1958), 87-89. MR 0102804 (21:1590)
  • [Br] W. Browder, The Kervaire invariant of framed manifolds and its generalization, Ann. of Math. (2) 90 (1969), 157-186. MR 0251736 (40:4963)
  • [HiHoRa] M. Hill, M. Hopkins and D. Ravenel, On the non-existence of elements of Kervaire invariant one, arXiv:0908.3724.
  • [Hi] F. Hirzebruch, ``Division algebras and topology'', in Numbers, Graduate Texts in Mathematics 123, Springer-Verlag, New York, 1991, pp. 281-302.
  • [Ho] H. Hopf, Über die Abbildungen von Sphären auf Sphären niedriger Dimension, Fund. Math. 25 (1935), 427-440.
  • [Ke] M. Kervaire, Non-parallelizability of the $ n$-sphere, $ n>7$, Proc. Nat. Acad. U.S.A. 44 (1958), 280-283.
  • [Mi] J. Milnor, Some consequences of a theorem of Bott, Ann. of Math. (2) 68 (1958), 444-449. MR 0102805 (21:1591)

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Additional Information

Andrew Ranicki
Affiliation: University of Edinburgh
Email: a.ranicki@ed.ac.uk

DOI: https://doi.org/10.1090/S0273-0979-2011-01345-3
Received by editor(s): May 25, 2011
Published electronically: June 14, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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