PL-Surfaces in Homology 4-Balls

The course explores the concept of manifold-knot pairs in homology 3-spheres that bound homology 4-balls. It discusses the existence of pairs where the knot does not bound a PL-disk in any bounding homology ball and demonstrates that the minimum genus of a PL surface in any bounding homology ball can be arbitrarily large. The teaching method involves presenting proofs based on Heegaard Floer homology. This course is intended for individuals interested in gauge theory and low-dimensional topology.