Smooth Yamabe invariant and surgery

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 number ${\Lambda }_n$, depending only on the dimension $n$ of $M$, such that $$\sigma (N)\ge \min \sigma (M),{\Lambda }_n.$$

Suggestions by the referee included. Improved results for 3-dimensional surgery on 6-dimensional manifolds. Version close to published version

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Cited by in corpus (7)

• Low-dimensional surgery and the Yamabe invariant
• The Yamabe problem on stratified spaces
• A note on Yamabe constants of products with hyperbolic spaces
• Relative K-area homology and applications
• Relative Yamabe invariant and c-concordant metrics
• Computations of the orbifold Yamabe invariant
• Results on the existence of the Yamabe minimizer of M^m \times R^n