Low-dimensional surgery and the Yamabe invariant
نویسندگان
چکیده
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), (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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