Abstract
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 constant $\Lambda_n$, depending only on the dimension n of $M$, such that \[ \sigma(N) \ge \mathrm{min}\{\sigma(M),\Lambda_n\}.\]
Citation
Bernd Ammann. Mattias Dahl. Emmanuel Humbert. "Smooth Yamabe invariant and surgery." J. Differential Geom. 94 (1) 1 - 58, May 2013. https://doi.org/10.4310/jdg/1361889060
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