Four-manifolds up to connected sum with complex projective planes

Abstract

We show that closed, connected 4-manifolds up to connected sum with copies of the complex projective plane are classified in terms of the fundamental group, the orientation character and an extension class involving the second homotopy group. For fundamental groups that are torsion free or have one end, we reduce this further to a classification in terms of the homotopy 2-type.

37 pages. v2: former sections 5 and 6 rewritten and split into current sections 5, 6, and 7. Accepted for publication in American Journal of Mathematics