Date: 10 March 2017, 4:30pm
Location: Hempfield High School, Room 213
 Speaker: Hannah Schwartz, Bryn Mawr College
 Title: Cork twists, and smooth structures on 4-manifolds
 

 Abstract. Examples of topological 4-manifolds with distinct
smooth structures abound, but characterizations of the full set of
smooth structures on a given 4-manifold remain elusive. It was proved in
the 1990's by Curtis-Freedman-Hsiang-Stong and Matveyev that any two
homeomorphic, closed, simply-connected smooth 4-manifolds are related by
removing and regluing a single compact contractible submanifold, called
a cork. After a preliminary discussion on the relevant background
(including examples of well-known corks), this talk will present joint
work with Paul Melvin that generalizes this result to any finite list of
homeomorphic, closed, simply-connected, smooth 4-manifolds. If time
permits, we shall also address infinite lists of homeomorphic, smooth
4-manifolds. In this case a strictly analogous theorem is not possible,
as noted recently by Tange and Yasui, but extensions can be obtained by
relaxing either the compactness or connectedness condition on the cork.