Instantons, Suspension, and Surgery - Part 1

Explore a conference talk on gauge theory and low-dimensional topology, focusing on the Dehn surgery number of oriented connected closed 3-manifolds. Delve into the groundbreaking research by Aliakbar Daemi and Miller Eismeier, which demonstrates the existence of integer homology 3-spheres with arbitrarily large Dehn surgery numbers. Examine the proof methodology, which utilizes Froyshov's q_3 invariant and mod 2 instanton homology. Investigate two crucial components of the proof: the computation of q_3 for connected sums of Poincare homology spheres and an inequality involving q_3 of a 3-manifold Y in relation to b^+ of a 4-manifold filling Y. Gain insights into the concept of suspensions of instanton Floer complexes and its application in this context.