# Trimok

 55 Reputation 45 views

## Registered User

 Name Trimok Member for 7 months Seen 18 hours ago Website Location France Age
 22h comment What is the 31th homotopy group of the 2 - sphere ?@Mark : Yes, I understand this is not the final answer... 23h comment What is the 31th homotopy group of the 2 - sphere ?I don't know if it is the correct result, but it seems that the answer should be $Z_2 + Z_2 + Z_2 + Z_2$ (Found page 204, in 1st paper reference below) Nobuyuki Oda, On the 2.Components of the Unstable Homotopy Groups of Spheres I. Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 53, Number 7 (1977), 215-218. [1st paper](projecteuclid.org/DPubS/Repository/1.0/…) 1d comment What is the 31th homotopy group of the 2 - sphere ?The beginning of the article can apparently be read on [Google Books](books.google.fr/…) 1d comment What is the 31th homotopy group of the 2 - sphere ?Thanks for the reference 1d comment What is the 31th homotopy group of the 2 - sphere ?@Mariano : I understand you, but there are also a lot of mathematical books, where the interesting ideas or philosophy are not highlighted, because it is hidden in a too formal or technical presentation. And, in mathematics or physics, the important things are ideas. 1d comment What is the 31th homotopy group of the 2 - sphere ?@Christian Nassau : OK, Thanks 1d comment What is the 31th homotopy group of the 2 - sphere ?@Christian Nassau : Thanks for the reference (I am going to see it I am able to extract information from this paper) 1d comment What is the 31th homotopy group of the 2 - sphere ?@David Roberts : Thanks, have you a reference, please ? 1d comment What is the 31th homotopy group of the 2 - sphere ?Yes, I know, but it is however possible, that there exists a link between this 31th homotopy group of the 2-sphere, and classification of 4-qbits entanglements. 1d comment What is the 31th homotopy group of the 2 - sphere ?In the reference physics article, it is explained that, in a Hopf fibration, the base space (S4,S8) contains information about one qbit, and the entanglement with the others qbits. If there is no entanglement, this reduces to S2. The third Hopf fibration explains 3-qbits entanglement, so it is hoped that sedenions (so S31) could explain 4-qbits entanglement. 1d asked What is the 31th homotopy group of the 2 - sphere ? Nov29 comment Dilogarithm, tetrahedrons, and hyperbolic spaceI agree, in fact here the non-trivial fact is that the five-term dilogarithm relation is linked to very specific 3-volumes in hyperbolic space (ABCD, ABCE, ABDE, ACDE, BCDE). So, yes, there is a 3-volume form which is closed.