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seen May 20 '13 at 10:04

May
24
awarded  Commentator
May
17
comment What is the 31th homotopy group of the 2 - sphere ?
@Mark : Yes, I understand this is not the final answer...
May
17
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
May
17
comment What is the 31th homotopy group of the 2 - sphere ?
The beginning of the article can apparently be read on Google Books
May
17
comment What is the 31th homotopy group of the 2 - sphere ?
Thanks for the reference
May
17
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.
May
17
comment What is the 31th homotopy group of the 2 - sphere ?
@Christian Nassau : OK, Thanks
May
17
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)
May
17
comment What is the 31th homotopy group of the 2 - sphere ?
@David Roberts : Thanks, have you a reference, please ?
May
17
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.
May
17
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.
May
17
asked What is the 31th homotopy group of the 2 - sphere ?
Nov
29
comment Dilogarithm, tetrahedrons, and hyperbolic space
I 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.
Oct
16
comment Building an invariant Sn structure from two invariant Zn structures
The quotes are there, because I am not sure at all of using the adequate mathematical language. But the idea is simple, it is just an interval in the boundary $S_1$ of the disk $D_2$, or, if you prefer, it is a part of $S_1$ parametrized by an angular interval. The important point is that these intervals are indexed, so there is an order.
Oct
12
revised Building an invariant Sn structure from two invariant Zn structures
edited title; added 1 characters in body; edited tags
Oct
12
asked Building an invariant Sn structure from two invariant Zn structures
Oct
8
accepted Surface of a Ideal Tetrahedron in Hyperbolic Space H3
Oct
8
comment Surface of a Ideal Tetrahedron in Hyperbolic Space H3
This is the first one : What is the surface area of the boundary of the tetrahedron? And Ok, the answer was given by Igor
Oct
6
awarded  Scholar
Oct
6
accepted Dilogarithm, tetrahedrons, and hyperbolic space