Braiding is easier in a restricted topology. That’s why research on anyons uses restricted topologies which cross world lines rather than trying to construct 2-

Braiding is easier in a restricted topology. That’s why research on anyons uses restricted topologies which cross world lines rather than trying to construct 2-knots in a 3+1D spacetime. As you approach a singularity, “around” becomes much shorter than “across”, effectively restricting the space you’re in. Around being shorter than across is why black holes form Einstein rings: the light is taking the shortest path! So if paths cross while going around the singularity, they can’t untangle by moving across the singularity. Hence you have an easier time building topological modes, akin to the restricted topologies for anyons. (Or so my conjecture goes.)