Smooth Yamabe invariant and surgery
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 Λn, depending only on the dimension n of M, such that
σ(N) ≥ min{σ(M),Λn}.

Mathematics Subject Classification

35J60 (Primary), 35P30, 57R65, 58J50, 58C40 (Secondary)


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