Smooth Yamabe invariant and surgery

We prove a surgery formula for the smooth Yamabe invariant $σ(M)$ of a compact manifold $M$. Assume that $N$ is obtained from $M$ by surgery of codimension at least 3. We prove the existence of a positive number $Λ_n$, depending only on the dimension $n$ of $M$, such that $σ(N) \geq \min{σ(M),Λ_n}.$

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