Unstable homotopy groups of spheres

From the bottom of this page you can download Mathematica programs that know many results about the unstable homotopy groups of spheres up to the 19-stem. Most of the information is taken from Toda's book "Composition methods in homotopy groups of spheres"; a few additional facts are proved in an accompanying note or quoted from elsewhere. The program does not do any serious calculations for itself, it is merely a convenient way of organizing and accessing results obtained by traditional methods. One can also do some automated consistency checking to detect any errors. I have tried to use a fairly general framework so that other computations in unstable homotopy can be included later if people are interested.

This program is not really finished, but I think it is already useful, and I have moved on to other things, so I have decided to release it.
Here are some examples of things one can type, and the program's response:


SpherePi[14,2]
Z2η5°ε6Z2μ5Z2ν5°ν8°ν11
HomotopySet[Sphere[7],Sphere[4]]
Zν4Z4ν′
GroupType[SpherePi[19,10]]
Z2Z2Z2Z
ShowMap[Hopf,8,4]
π84
π87
Z2ν4°η7Z2(Σν′)°η7
Z2η7
ν4°η7
η7
(Σν′)°η7
0
ShowMap[Sigma,To[sigmaprime]]
π136
π147
Z4σ"
Z8σ′
σ"
2 σ′
Explain[o[nuprime,nu[7]]]
ν′°ν7 → 0
This takes place in the trivial group π10S3 - see Todas Proposition 5.15

Files

To use the program: Here are the files: