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

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
HTML articles powered by AMS MathViewer

by Andrew Ranicki PDF

Bull. Amer. Math. Soc. 48 (2011), 509-511 Request permission

References

J. F. Adams, On the nonexistence of elements of Hopf invariant one, Bull. Amer. Math. Soc. 64 (1958), 279–282. MR 97059, DOI 10.1090/S0002-9904-1958-10225-6
J. F. Adams, On the non-existence of elements of Hopf invariant one, Ann. of Math. (2) 72 (1960), 20–104. MR 141119, DOI 10.2307/1970147
J. F. Adams and M. F. Atiyah, $K$-theory and the Hopf invariant, Quart. J. Math. Oxford Ser. (2) 17 (1966), 31–38. MR 198460, DOI 10.1093/qmath/17.1.31
R. Bott and J. Milnor, On the parallelizability of the spheres, Bull. Amer. Math. Soc. 64 (1958), 87–89. MR 102804, DOI 10.1090/S0002-9904-1958-10166-4
William Browder, The Kervaire invariant of framed manifolds and its generalization, Ann. of Math. (2) 90 (1969), 157–186. MR 251736, DOI 10.2307/1970686
M. Hill, M. Hopkins and D. Ravenel, On the non-existence of elements of Kervaire invariant one, arXiv:0908.3724.
F. Hirzebruch, “Division algebras and topology”, in Numbers, Graduate Texts in Mathematics 123, Springer-Verlag, New York, 1991, pp. 281–302.
H. Hopf, Über die Abbildungen von Sphären auf Sphären niedriger Dimension, Fund. Math. 25 (1935), 427–440.
M. Kervaire, Non-parallelizability of the $n$-sphere, $n>7$, Proc. Nat. Acad. U.S.A. 44 (1958), 280–283.
John Milnor, Some consequences of a theorem of Bott, Ann. of Math. (2) 68 (1958), 444–449. MR 102805, DOI 10.2307/1970255