Counterexamples in 4-manifold topology

Abstract

We illustrate the rich landscape of 4-manifold topology through the lens of counterexamples. We consider several of the most commonly studied equivalence relations on 4-manifolds and how they are related to one another. We explain implications e.g. that $h$-cobordant manifolds are stably homeomorphic, and we provide examples illustrating the failure of other potential implications. The information is conveniently organised in a flowchart and a table.