##  [Freudenthal Suspension Theorem](/index.php/freudenthal-suspension-theorem) 

  ##  [Freudenthal Suspension Theorem](https://puremath.quantumdictionary.io/freudenthal-suspension-theorem-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A theorem describing how suspension stabilizes homotopy groups: for a sufficiently connected space X, the suspension homomorphism π_k(X) → π_{k+1}(ΣX) is an isomorphism in a range determined by the connectivity of X and is surjective slightly beyond that range, which leads to stable homotopy groups after iterated suspension.