Quaternionic projective space | Wikipedia audio article
Channel: wikipedia tts
Date: 03/05/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Quaternionic_projective_space


00:00:59 1 In coordinates
00:05:39 2 Topology
00:05:48 2.1 Homotopy theory
00:09:55 3 Differential geometry
00:11:28 3.1 Characteristic classes
00:13:47 4 Special cases
00:13:56 4.1 Quaternionic projective line
00:15:02 4.2 Quaternionic projective plane



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SUMMARY
=======
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
        
        .
      
    
    {\displaystyle \mathbb {H} .}
   Quaternionic projective space of dimension n is usually denoted by

  
    
      
        
          
            H
            P
          
          
            n
          
        
      
    
    {\displaystyle \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. The quaternionic projective line 
  
    
      
        
          
            H
            P
          
          
            1
          
        
      
    
    {\displaystyle \mathbb {HP} ^{1}}
   is homeomorphic to the 4-sphere.