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 S³ and S²-bundles over S¹.