I took my qualifying (oral) exam in Fall 2019. My committee members were Mark McLean, John Morgan, and Olga Plamenevskaya. Here is a document with questions I thought would be fair to ask as well as a transcript of the actual exam. Below are some notes I wrote up to help me study. Please let me know if you spot errors.
The main source for the major topic was Morse Theory and Floer Homology by M. Audin and M. Damian. It is an excellent book and so my notes have little to add to their treatment. Perhaps the main downside of the text is that it's fairly lengthy. Hence, in preparing for the exam, I found it helpful to condense material into these notes.
For the minor topic, I mostly referred to John Morgan's The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. It was also helpful to use his notes in Gauge Theory and the Topology of Four-Manifolds and Lawson and Michelsohn's Spin Geometry. As above, all these sources are already excellent and my goal was mainly to condense them.
Perhaps because of the pressure of the exam, my mind cracked a bit and I
wrote something entitled: "If
Complex Geometry Became a Gladitorial Sport."