We explore how contractible pieces inside 4-manifolds can magically change smooth structures when removed and reglued. Starting from the Mazur cork, we take a tour through our 4-manifold zoo and meet some interesting exotic pairs that differ only by a cork twist. There may also be infinite families of such examples (involving infinite-order corks).
A spork, on the other hand, is a contractible piece together with a boundary map that extends over the interior, so the twist does nothing exotic. As part of our training program to work at this zoo, we will practice seeing how the Mazur cork is just one “click” away from a spork.