On [Wikipedia][1], it is said that the minimal volume 

$$\operatorname{MinVol}(M):=\inf\{\operatorname{vol}(M,g) :g\text{ a complete Riemannian metric with }|K_{g}|\leq 1\}$$

is a topological invariant, introduced by [Gromov][2].

I have no doubt that this concept was introduced by Gromov, but I am having my doubts that this is really a topological invariant. That would mean that homeomorphic manifolds have the same minimal volume and that seems too good to be true. So, is the minimal volume invariant under homeomorphisms?

I apologize if this question is too basic for mathoverflow... in that case I will reask it on math.stackexchage.


  [1]: https://en.wikipedia.org/wiki/Minimal_volume
  [2]: https://en.wikipedia.org/wiki/Mikhael_Gromov_(mathematician)