##  [Mapping Torus](/mapping-torus) 

  ##  [Mapping Torus](https://puremath.quantumdictionary.io/mapping-torus-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The quotient space obtained from X × [0,1] by identifying (x,1) with (f(x),0) for a self-map f: X → X; it is a space that fibers over the circle S1 with fiber X and monodromy f.