##  [Fundamental Group](/fundamental-group) 

  ##  [Fundamental Group](https://puremath.quantumdictionary.io/fundamental-group-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The group π1(X, x0) of homotopy classes of based loops at a chosen basepoint x0 in a topological space X, with group law given by concatenation of loops; it captures the 1-dimensional homotopy/hole structure of X.