The strong Haken theorem via sphere complexes (Q6614585)

Heegaard splittings play an important role in the study of \(3\)-manifolds. In the paper under review, the authors ``give a short proof of Scharlemann's strong Haken theorem for closed \(3\)-manifolds (and manifolds with spherical boundary). As an application, we also show that given a decomposing sphere \(R\) for a \(3\)-manifold \(M\) that splits off an \(S^{2}\times S^{1}\) summand, any Heegaard splitting of \(M\) restricts to the standard Heegaard splitting on the summand.''