Kyle Hayden (Rutgers - Newark): Exotic 4-manifolds and the complexity of h-cobordisms

Abstract: Work of Wall and Gompf revealed that any two smooth structures on a compact, orientable 4-manifold become diffeomorphic after connected sums with enough copies of S²xS². A longstanding question raised by Wall asks whether a single copy suffices, at least when the 4-manifold is closed and simply connected. In this talk, I will discuss an elementary approach to studying this "instability" of exotic phenomena through the lens of h-cobordisms. In particular, I will describe a simple criterion for detecting non-minimal h-cobordisms and explain how it suggests a strategy for constructing potential counterexamples to Wall’s question and some of its variants.