# Smooth Yamabe invariant and surgery

by

Bernd Ammann, Mattias Dahl, Emmanuel Humbert

**Smooth Yamabe invariant and surgery**
(.pdf)

*J. Diff. Geom.* **94**, *1-58* (2013)

We prove a surgery formula for the smooth Yamabe invariant σ(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 Λ_{n}, depending only on the dimension n of M, such that σ(N) ≥ min{σ(M),Λ_{n}}.
35J60 (Primary), 35P30, 57R65, 58J50, 58C40 (Secondary)
### Keywords

Yamabe invariant, surgery, positive scalar curvature
### Typo in printed version

At the end of section 1.4, the index *≥3 should be replaced by *≥5
at several locations. The whole section is only valid for dimension
at least 5, which was repeated at various places, and which applies also
to the end of secion 1.4.

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The Paper was written on April 4, 2008

Last update Sep 12, 2012