What is $\pi_{31}(S^2)$, the 31th homotopy group of the 2 - sphere ?
This question has a physics motivation:
There are relations between (2nd and 3rd) Hopf fibrations and (2- and 3-) qbits (quantum bits) entanglement, see this reference
Maybe there are relations between classification of qbits entanglements and sphere homotopy groups, and we are interested in the classification of 4-qbits entanglements.
I tried fo find the solution on the net, with help of math fans, but without success.
Wikipedia gives only to the 22th group homotopy of the 2-sphere
This article of John Baez gives interesting references, like Allen Hatcher, Stable homotopy groups of spheres or a link with braids. One speak of a book of Kochman Stanley O. : Stable Homotopy Groups of Spheres A Computer-Assisted Approach
But I am totally unable to find the answer.
A subsidiary question would be : Until what rank do we know these high homotopy group of the 2-sphere ?