現代数学の系譜11 ガロア理論を読む8

現代数学の系譜11 ガロア理論を読む8at MATH

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552:545
 14/05/24 03:52:04.90 
>>548 
専ブラでなくても名前は入れられる

553:１３２人目の素数さん
 14/05/24 06:43:17.92 
>>552 
ども 
名前は入れられるが、面倒なので省略しています

554:１３２人目の素数さん
 14/05/24 10:34:41.47 
>>550 
補足 
こういうことみたい 
 
http://en.wikipedia.org/wiki/N-sphere#Spherical_coordinates 
An n-sphere is the surface or boundary of an (n + 1)-dimensional ball, and is an n-dimensional manifold.  
For n ≥ 2, the n-spheres are the simply connected n-dimensional manifolds of constant, positive curvature.  
The n-spheres admit several other topological descriptions:  
for example, they can be constructed by gluing two n-dimensional Euclidean spaces together, by identifying the boundary of an n-cube with a point,  
or (inductively) by forming the suspension of an (n － 1)-sphere. 
 
4-sphere  
    Equivalent to the quaternionic projective line, HP1. SO(5)/SO(4). 
 
http://en.wikipedia.org/wiki/Quaternionic_projective_line 
In mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space,  
to the case where coordinates lie in the ring of quaternions H. Quaternionic projective space of dimension n is usually denoted by 
 
    \mathbb{HP}^n 
 
and is a closed manifold of (real) dimension 4n. It is a homogeneous space for a Lie group action, in more than one way. 
 
Projective line 
From the topological point of view the quaternionic projective line is the 4-sphere, and in fact these are diffeomorphic manifolds.  
The fibration mentioned previously is from the 7-sphere, and is an example of a Hopf fibration.

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