Low-dimensional surgery and the Yamabe invariant

Details Low-dimensional surgery and the Yamabe invariant Low-dimensional surgery and the Yamabe invariant

2012-04-05

arxiv.org/abs/1204.1197v1

Mathematics

Geometric Topology

Scientific paper

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

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