- Series
- Geometry Topology Seminar
- Time
- Monday, October 7, 2019 - 2:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Paul Melvin – Bryn Mawr College
- Organizer
- Caitlin Leverson

It is a remarkable fact that some compact topological 4-manifolds X admit infinitely many exotic smooth structures, a phenomenon unique to dimension four. Indeed a fundamental open problem in the subject is to give a meaningful description of the set of all such structures on any given X. This talk will describe one approach to this problem when X is simply-connected, via cork twisting. First we'll sketch an argument to show that any finite list of smooth manifolds homeomorphic to X can be obtained by removing a single compact contractible submanifold (or cork) from X, and then regluing it by powers of a boundary diffeomorphism. In fact, allowing the cork to be noncompact, the collection of all smooth manifolds homeomorphic to X can be obtained in this way. If time permits, we will also indicate how to construct a single universal noncompact cork whose twists yield all smooth closed simply-connected 4-manifolds. This is joint work with Hannah Schwartz.