Smooth Yamabe invariant and surgery

By Bernd Ammann, Mattias Dahl, E. Humbert. 2008

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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 $$ \sigma(N) \geq \min\{\sigma(M),\Lambda_n\}. $$

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4557cf7602e51754f6c5b10bba2d5e47c398bfc0