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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(s):
Andrew
Ranicki
Journal:
Bull. Amer. Math. Soc.
48
(2011),
509-511.
MSC (2010):
Primary 57R22, 17A35
Posted:
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.
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Additional information
References:
-
- [Ad1]
- J. F. Adams, On the nonexistence of elements of Hopf invariant one, Bull. Amer. Math. Soc. 64 (1958), 279-282. MR 0097059 (20:3539)
- [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,
 -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
 -sphere,  , 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:
10.1090/S0273-0979-2011-01345-3
PII:
S 0273-0979(2011)01345-3
Received by editor(s):
May 25, 2011
Posted:
June 14, 2011
Copyright of article:
Copyright
2011,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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