Stable diffeomorphism of compact 4-manifolds
The author proves that if two closed smooth orientable 4-manifolds M and N are homeomorphic they are stably diffeomorphic i.e. there exists \(r\in {\mathbb{N}}\) such that M{\#}r(S\({}^ 2\times S^ 2)\) is diffeomorphic to N{\#}r(S\({}^ 2\times S^ 2)\). The same result holds for nonorientable manifolds if M and N are replaced by the connected sum with the nontrivial \(S^ 2\)-bundle over \(S^ 2\). The proof is based on the construction of ''bad'' smoothings of some simple manifolds which together with results of Quinn reduces the problem to stable smoothing theory of Lashof and Shaneson. The ''bad'' smoothings are constructed with the help of Freeman's classification of 1-connected 4-manifolds. (The reviewer has in 1982 independently obtained a slight generalization of these results. This will be published in a book with the title ''Surgery and duality''.)
scientific article; zbMATH DE number 3947229