This is a cross post of [MSE][1].

>**Q1:** What does "**irreducible manifold**" mean (not definition)?

My understanding of "irreducible manifold" is "is not reducible (homotopic or deformation or homeomorph or being prime manifold or something like these) to other manifold". If so, what is the meaning (definition) of reducible manifold?

>**Q2:** What is the origin of this terminology?
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>**Q3:** Is there any Book or expository paper about irreducible manifolds in higher dimensions?


  [1]: https://math.stackexchange.com/q/3432171/272127