##  [Thom Isomorphism](/thom-isomorphism) 

  ##  [Thom Isomorphism](https://puremath.quantumdictionary.io/thom-isomorphism-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A statement in algebraic topology that for a (suitably oriented) rank‑k vector bundle E → B there exists a Thom class in the cohomology of the Thom space Th(E) that induces an isomorphism H^*(B; R) → H^{*+k}(Th(E); R) (equivalently H^*(Th(E)) ≅ H^{*-k}(B) after degree shift), enabling transfer and Gysin maps.