Online Talk 

Zoom link: https://princeton.zoom.us/j/453512481?pwd=OHZ5TUJvK2trVVlUVmJLZkhIRHFDUT09

To a positive definite four-manifold with lens space boundary, one may glue a plumbing of spheres to produce an embedding of this plumbing in a closed, positive definite four-manifold. This construction was used by Lisca to classify those lens spaces bounding rational homology balls, and by Greene to classify those lens spaces coming from integer surgery on a knot. In this talk, I will describe how to use this idea in the other direction, starting from an embedding of a plumbing of spheres and taking a complement to arrive at a manifold with lens space boundary. This results in many examples of simply-connected four-manifolds with $b_2 = 1$ and lens space boundary, most of which cannot be built by attaching a single two-handle to $B^4$. Variants of these constructions also produce smoothly embedded spheres representing several homology classes in connected sums of $\mathbb{C} P^2$, and I will discuss a conjecture on exactly which homology classes support a smoothly embedded sphere.