Splitting obstruction groups in codimension 2 (Q5951069)

The problem of splitting a manifold (more generally a Poincaré complex) along a codimension \(2\) submanifold (subcomplex) is considered. Codimension \(1\) splitting problems were already treated successfully by many authors. The case of a splitting with codimension \(>2\) depends only on the abstract surgery obstruction group of the fundamental group of the submanifold. In the paper under review, some new exact sequences involving surgery groups, Wall groups and splitting obstruction groups are obtained. Computations of splitting obstruction groups of specific examples are done.