Smooth Yamabe invariant and surgery

Details Smooth Yamabe invariant and surgery Smooth Yamabe invariant and surgery

2008-04-09

arxiv.org/abs/0804.1418v3

Mathematics

Differential Geometry

The new version contains new topological applicatins

Scientific paper

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 $$ \sigma(N)
\geq \min\{\sigma(M),\Lambda_n\}. $$

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