##  [Pontryagin–Thom Construction](/pontryagin-thom-construction) 

  ##  [Pontryagin–Thom Construction](https://puremath.quantumdictionary.io/pontryagin-thom-construction-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A geometric procedure that associates to a properly embedded, framed submanifold (or cobordism class) of a high‑dimensional sphere a homotopy class of maps into a Thom space (or a sphere after stabilization), thereby converting geometric bordism and embedding questions into questions about homotopy groups.