Alex Zupan, University of Nebraska, A special case of the Smooth 4-dimensional Poincare Conjecture
The smooth version of the 4-dimensional Poincare Conjecture (S4PC) states that every homotopy 4-sphere is diffeomorphic to the standard 4-sphere. One way to attack the S4PC is to examine a restricted class of 4-manifolds. For example, Gabai's proof of Property R implies that every homotopy 4-sphere built with one 2-handle and one 3-handle is standard. …