|
| |
|
|
A048648
|
|
Order of n-th stable homotopy group of spheres.
|
|
3
| |
|
|
2, 2, 24, 1, 1, 2, 240, 4, 8, 6, 504, 1, 3, 4, 960, 4, 16, 16, 528, 24, 4, 4, 1048320, 4, 4, 12, 24, 2, 1, 2, 32640, 4, 64
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Proved by Serre to be finite for all positive n.
|
|
|
REFERENCES
| D. B. Fuks, "Spheres, homotopy groups of the", Encyclopaedia of Mathematics, Vol. 8.
S. O. Kochman, Stable homotopy groups of spheres. A computer-assisted approach. Lecture Notes in Mathematics, 1423. Springer-Verlag, Berlin, 1990. 330 pp. ISBN: 3-540-52468-1. [Math. Rev. 91j:55016]
S. O. Kochman and M. E. Mahowald, On the computation of stable stems. The Cech Centennial (Boston, MA, 1993), 299-316, Contemp. Math., 181, Amer. Math. Soc., Providence, RI, 1995. [Math. Rev. 96j:55018]
Robert Scharein's program sphere-link.c linked from www.pims.math.ca/knotplot/links/sphere.html
|
|
|
LINKS
| A. Hatcher, Stable Homotopy Groups of Spheres
John W. Milnor, Differential Topology Forty-six Years Later, Notices Amer. Math. Soc. 58 (2011), 804-809.
Wikipedia, Homotopy groups of spheres
|
|
|
FORMULA
| a(n) = |Pi_n^S| = |Pi_{k+n}(S^k)| for k > n+1.
|
|
|
EXAMPLE
| Pi_1^S = Pi_4(S^3) = Z/2Z, so a(1) = |Z/2Z| = 2.
|
|
|
CROSSREFS
| Cf. A001676.
Sequence in context: A014358 A093355 A122962 * A120065 A131448 A156447
Adjacent sequences: A048645 A048646 A048647 * A048649 A048650 A048651
|
|
|
KEYWORD
| nonn,nice
|
|
|
AUTHOR
| Stephen A. Silver (maths(AT)argentum.freeserve.co.uk)
|
|
|
EXTENSIONS
| More terms from Alex Fink (finka(AT)math.ucalgary.ca), Aug 10 2006
|
| |
|
|
