# Low-dimensional surgery and the Yamabe invariant

by

Bernd Ammann, Mattias Dahl, Emmanuel Humbert

**Low-dimensional surgery and the Yamabe invariant**
.pdf)

*J. Math. Soc. Japan* **67**, *159-182* (2015)

Assume that M is a compact n-dimensional manifold and that N is obtained by surgery along a k-dimensional sphere, k≤n-3. The smooth Yamabe invariants σ(M) and σ(N) satisfy σ(N)≥ min (σ(M),Λ) for Λ>0. We derive explicit lower bounds for Λ in dimensions where previous methods failed, namely for (n,k)∈{(4,1),(5,1),(5,2),(6,3),(9,1),(10,1)}. With methods from surgery theory and bordism theory several gap phenomena for smooth Yamabe invariants can be deduced.
### Small typo in the published version

- In Example 4.12 the conclusion should be: "and we conclude that Λ
_{6,3} >49.98"

In the pdf-version above we have corrected this obvious typo.

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The Paper was written on 4.4.2012

Last update 9.5.2022