Seifert fiber space | Wikipedia audio article
Channel: wikipedia tts
Date: 17/05/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Seifert_fiber_space


00:00:40 1 Definition
00:02:41 2 Classification
00:08:43 3 Fundamental group
00:09:03 4 Positive orbifold Euler characteristic
00:15:36 5 Zero orbifold Euler characteristic
00:17:05 6 Negative orbifold Euler characteristic
00:20:48 7 References
00:26:23 1 is homeomorphic to {0; (n1, 1); (2, 1), (2, 1)}. The first homology is Z+Z/2Z+Z/2Z if b=0, and Z+Z/4Z if b=1. These two Klein bottle bundle are surface bundles associated to  the y-homeomorphism and the product of this and the twist.
00:26:51 Negative orbifold Euler characteristic



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SUMMARY
=======
A Seifert fiber space is a 3-manifold together with a "nice" decomposition as a disjoint union of circles. In other words, it is  a 
  
    
      
        
          S
          
            1
          
        
      
    
    {\displaystyle S^{1}}
  -bundle (circle bundle) over a 2-dimensional  orbifold. Most "small" 3-manifolds are Seifert fiber spaces, and they account for all compact oriented manifolds in 6 of the 8 Thurston geometries of the geometrization conjecture.