**Defintion:**
a $n$-manifold $M$ is said rigid if any homotopy equivalence $M\rightarrow N$ is homotopic to a homemorphism, where $N$ is an $n$-manifold.

The sphere $S^{3}$ and hyperbolic compact oriented $3$-manifold (without boundary) and the torus $T^{3}$ are rigid if I'm not wrong.

**Question:**
More generally, suppose that $M$ is a compact oriented $3$-manifold (without boundary) is it rigid ?

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