# Low-dimensional surgery and the Yamabe invariant

by

Bernd Ammann, Mattias Dahl, Emmanuel Humbert

**Low-dimensional surgery and the Yamabe invariant**
(.dvi, .ps,.ps.gz or .pdf)

*J. Math. Soc. Japan* **67**, *159-182* (2015)

Assume that M is a compact n-dimensional manifold and that N is obtained by surgery along a k-dimensional sphere, k≤n-3. The smooth Yamabe invariants σ(M) and σ(N) satisfy σ(N)≥ min (σ(M),Λ) for Λ>0. We derive explicit lower bounds for Λ in dimensions where previous methods failed, namely for (n,k)∈{(4,1),(5,1),(5,2),(6,3),(9,1),(10,1)}. With methods from surgery theory and bordism theory several gap phenomena for smooth Yamabe invariants can be deduced.

Zurück zur Homepage

The Paper was written on 4.4.2012

Last update 12.3.2013