Connected sums with HP^n or CaP^2 and the Yamabe invariant

Let $M$ be a smooth closed $4k$-manifold whose Yamabe invariant $Y(M)$ is nonpositive. We show that $Y(M\sharp l \Bbb HP^k\sharp m \bar{\Bbb HP^k})=Y(M),$ where $l,m$ are nonnegative integers, and $\Bbb HP^k$ is the quaternionic projective space. When $k=4$, we also have $Y(M\sharp l CaP^2\sharp m \bar{CaP^2})=Y(M),$ where $CaP^2$ is the Cayley plane.

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