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 ?