A generalization of the Wang sequence (Q719060)

A smooth manifold \(M\) is said to have focal genus 2 if it admits a decomposition given by gluing two disc bundles over manifolds \(N_{1}\) and \(N_{2}\) along their boundaries together. Then by means of the obvious zero section embeddings, \(N_{1}\) and \(N_{2}\) can be identified as submanifolds of \(M\), which are called focal submanifolds. The author analyzes these manifolds very creatively, so that he can extend the classical Wang sequence to a more generalized setting via regarding some given manifold as a manifold having focal genus 2 with two focal submanifolds.