We show that that a closed orientable $3$-manifold with a Heegaard splitting of genus $0$ or $1$ is either $\Bbb S^3$, a lens space, or $\Bbb S^2\times \Bbb S^1$.
$\text{MCG}(\Bbb S^1\times \Bbb S^1)$; Heegaard splitting of $\Bbb S^3$, lens space, etc.