On codimension two and one splitting
According to Cappell and Shaneson, very often the secondary surgery obstruction \(O_2\) to codimension two splitting is zero, but examples with \(O_2\neq 0\) exist. By considering homotopy equivalences with codomain the total space of a two disk bundle, the autor produces many examples with \(O_2\neq 0\) and other examples with \(O_2=0\). The approach is to compare codimension two splittings with codimension one splittings.
scientific article; zbMATH DE number 988057