Quinn’s transverse spheres lemma

In this first out of three talks, we will explain in detail the transverse spheres lemma by Quinn, which is the key geometric result that allows for the separation of infinitely many locally finite immersed 2-discs in a non-compact 4-manifold. The phenomena coming out of this lemma also allow one to understand why Quinn’s proof of this separation of infinite data is as complex as it is. We will explain these phenomena for future reference.