Smooth Yamabe invariant and surgery

Bernd Ammann; Mattias Dahl; Emmanuel Humbert

Smooth Yamabe invariant and surgery

Differential Geometry 2013-03-13 v5

Authors: Bernd Ammann , Mattias Dahl , Emmanuel Humbert

Abstract

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

Keywords

yamabe problem

Cite

@article{arxiv.0804.1418,
  title  = {Smooth Yamabe invariant and surgery},
  author = {Bernd Ammann and Mattias Dahl and Emmanuel Humbert},
  journal= {arXiv preprint arXiv:0804.1418},
  year   = {2013}
}

Comments

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

Smooth Yamabe invariant and surgery

Abstract

Keywords

Cite

Comments

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