##  [Homological Perturbation Lemma](/homological-perturbation-lemma) 

  ##  [Homological Perturbation Lemma](https://algebra.quantumdictionary.io/homological-perturbation-lemma-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A result and computational method that allows one to transfer a perturbation of a differential on a chain complex across a homotopy equivalence (given explicit homotopy data) to obtain a perturbed differential on a simpler model, preserving homotopy type.