  Lei and Wu have given a description of the second homotopy group of a closed
orientable 3-manifold in terms of the kernels of the epimorphisms from the
fundamental group of a Heegaard splitting surface onto the fundamental groups
of the two handlebody sides. In this note, we give a geometric derivation of
this result and collect some observations about the relation between the
various groups and the topology of the 3-manifold and the Heegaard splitting.
