Back in the 1990s, Mrowka and Kronheimer investigated what happens when you excise a two-dimensional surface from a four-dimensional manifold. If the manifold itself is simply connected, what conditions must surfaces meet to guarantee that their complements must also be simply connected? Kronheimer and Mrowka knew that some kinds of surfaces could have complements that weren’t simply connected. But their work seemed to indicate that another broad class of surfaces must always have simply connect...