##  [Fenchel–Nielsen Coordinates](/fenchel-nielsen-coordinates) 

  ##  [Fenchel–Nielsen Coordinates](https://puremath.quantumdictionary.io/fenchel-nielsen-coordinates-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A global system of real coordinates on Teichmüller space obtained by choosing a pants decomposition of a surface and recording, for each curve in the decomposition, a positive length parameter (the geodesic length) and a real twist parameter (amount of relative twist), together yielding 6g−6 real coordinates for a closed surface of genus g≥2.