##  [Ambient Isotopy](/ambient-isotopy) 

  ##  [Ambient Isotopy](https://puremath.quantumdictionary.io/ambient-isotopy-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A continuous one-parameter family of homeomorphisms H_t: M → M, t ∈ [0,1], of an ambient space M with H_0 = id_M such that H_1 carries one embedding or submanifold A ⊂ M to another embedding or submanifold B ⊂ M. Two embeddings are ambiently isotopic if they are related by such a family.