A note on Hempel-McMillan coverings of 3-manifolds

J. C. Gomez-Larranaga, F. Gonzalez-Acuna, W. Heil

Motivated by the concept of *A*-category of a manifold introduced
by Clapp and Puppe, we give a different proof of a (slightly generalized)
Theorem of Hempel and McMillan: if *M* is a closed 3-manifold that
is a union of three open punctured balls then *M* is a connected
sum of *S*^{3} and *S*^{2}-bundles over
*S*^{1}.