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)

Abstract

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