LACK OF DISJOINTNESS IN GENUS-1 SURFACES: THE PUNCTURED BALLOON THEOREM
Arturo Tozzi · viXra · 2021
Take a balloon, that is a genus-one manifold. If you break the jointness by piercing its surface, the hole gest lost and the punctured balloon becomes a genus-0 manifold. Starting from this trivial claim, we prove a topological theorem which plainly states that “the ends of a donut can meet, whilst the ends of a kidney pie cannot”. In this succinct note, we discuss the theorem and its implications in disparate topics such as topological connectedness, gauge theories and the physics of the black holes.