Obstructions to splitting manifolds with infinite fundamental group (Q1387310)

Let \(X \subset Y\) be a pair of smooth or piecewise smooth manifolds. The universally repelling square \(F\) of the oriented fundamental groups is called geometric if the maps \(\pi_1(\partial U) \rightarrow \pi_1(Y\smallsetminus X)\) and \(\pi_1(X) \rightarrow \pi_1(Y)\) are surjective, where \(U\) is a tubular neighbourhood of \(X\) in \(Y\). The authors calculate the corresponding obstruction groups in the special case that \(X\) has codimension \(1\) and the fundamental group of \(X\) is isomorphic to \(\mathbb Z\) or \(\mathbb Z \oplus \mathbb Z/2\).