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Smooth Yamabe invariant and surgery · arXivDesk

0804.1418Apr 9, 2008Suggestions by the referee included. Improved results for 3-dimensional surgery on 6-dimensional manifolds. Version close to published version

Smooth Yamabe invariant and surgery

Bernd Ammann, Mattias Dahl, Emmanuel Humbert

Differential Geometry

Abstract

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 $Λ_n$

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, depending only on the dimension

n

of

M

, such that

σ(N) \geq \min{σ(M),Λ_n}.

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