##  [Morse Theory](/morse-theory) 

  ##  [Morse Theory](https://puremath.quantumdictionary.io/morse-theory-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A technique linking the differential topology of a smooth manifold to the critical points of smooth real‑valued functions (Morse functions) on it: nondegenerate critical points have well‑defined indices and correspond to handle attachments that build the manifold, and Morse inequalities relate counts of critical points to homology.