3-manifolds with Yamabe invariant greater than that of $\Bbb{RP}\sp 3$
3-manifolds with Yamabe invariant greater than that of $\Bbb{RP}\sp 3$
We show that, for all nonnegative integers $k, l, m$ and $ n$, the Yamabe invariant of $$ \#(\mathbb{RP}^3)\# \ell(\mathbb{RP}^2 \#m(S^2 \times S^1)\#n(S^2 \tilde \times S^1)$$ is equal to the Yamabe invariant of $\mathbb{RP}^3$, provided $k + \ell \geq 1$. We then complete the classification (started by Bray and the …