Fiber 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/Fibered_manifold


00:01:05 1 History
00:02:24 2 Formal definition
00:02:51 3 Examples
00:03:44 4 Properties
00:04:29 5 Fibered coordinates
00:04:53 6 Local trivialization and fiber bundles
00:05:00 7 See also
00:05:11 8 Notes
00:09:06 9 References
00:09:53 9.1 Historical
00:11:32 10 External links
00:11:39 See also



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SUMMARY
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In differential geometry, in the category of differentiable manifolds, a fibered manifold is a surjective submersion

  
    
      
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    {\displaystyle \pi \colon E\to B\,}
  i.e. a surjective differentiable mapping such that at each point y ∈ E the tangent mapping

  
    
      
        
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    {\displaystyle T_{y}\pi \colon T_{y}E\to T_{\pi (y)}B}
  is surjective, or, equivalently, its rank equals dim B.