Joint Los Angeles Topology Seminar

We consider manifold-knot pairs (Y, K) where Y is a homology 3-sphere that bounds a homology 4-ball. Adam Levine proved that there exists pairs (Y, K) such that K does not bound a PL-disk in any bounding homology ball. We show that the minimum genus of a PL surface S in any bounding homology ball can be arbitrarily large. The proof relies on Heegaard Floer homology. This is joint work with Matthew Stoffregen and Hugo Zhou.