Smooth Yamabe invariant and surgery
Résumé
We prove a surgery formula for the smooth Yamabe invariant $\sigma(M)$ 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 $\Lambda_n$, depending only on the dimension $n$ of $M$, such that $$ \sigma(N) \geq \min\{\sigma(M),\Lambda_n\}. $$
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