New answers tagged 4-manifolds
The weaker version is a result due to Wall: C.T.C. Wall, On simply connected 4-manifolds, J. London Math. Soc., 39 (1964), 141–149 A stronger statement has been proven by Kreck (who also gives some references), but I don't know about the original reference Gompf and Stipsicz were thinking about. Matthias Kreck, h-cobordisms between 1-...
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