Van Kampen's theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-02-18

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Seifert%E2%80%93van_Kampen_theorem


00:00:38 1 Van Kampen's theorem for fundamental groupssup&#91;1&#93;/sup
00:03:20 1.1 Van Kampen's theorem for fundamental groupoids
00:09:15 2 Equivalent formulations
00:15:23 3 Examples
00:15:33 3.1 2-Sphere
00:17:54 3.2 Wedge Sum of Spaces
00:19:20 3.3 Orientable Genus g Surfaces
00:27:13 4 Generalizations
00:29:33 5 See also



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SUMMARY
=======
In mathematics, the Seifert–van Kampen theorem of algebraic topology (named after Herbert Seifert and Egbert van Kampen), sometimes just called van Kampen's theorem,  expresses the structure of the fundamental group of a topological space 
  
    
      
        X
      
    
    {\displaystyle X}
   in terms of the fundamental groups of two open, path-connected subspaces that cover 
  
    
      
        X
      
    
    {\displaystyle X}
  . It can therefore be used for computations of the fundamental group of spaces that are constructed out of simpler ones.