##  [Handle Decomposition](/handle-decomposition) 

  ##  [Handle Decomposition](https://puremath.quantumdictionary.io/handle-decomposition-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A procedure for building or analysing an n‑dimensional manifold by successively attaching k‑handles (D^k × D^{n−k}) for k = 0,1,...,n along attaching maps on the boundary; handle decompositions often arise from Morse functions where each nondegenerate critical point of index k corresponds to the attachment of a k‑handle.