##  [Elementary Collapse](/elementary-collapse) 

  ##  [Elementary Collapse](https://puremath.quantumdictionary.io/elementary-collapse-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A simplicial operation that removes a free face σ together with its unique coface τ from a simplicial complex K, where σ is a face of τ and σ is contained in no other maximal simplex; performing such an elementary collapse yields a new complex K' that is simple-homotopy equivalent to K.