I hope filing this under "Morse theory" is correct.
For the "abstract tensor" approach to knot theory you need: a) a 4D tensor to emulate particle interaction, b) a 2D tensor to emulate pair creation/annihilation. (I formulate it in Feynman diagram terms.) You don't actually need c) a particle propagator since this is the delta function.
Now you can rotate a knot by 90 degrees and you can rotate a Feynman diagram by 90 degrees, but you can't "rotate Morse theory by 90 degrees"! And I find this extremely annoying. A "nice" abstract tensor Sabcd emulating a crossing should have exactly the same symmetry properties as a crossing, i.e. invariance under all 180 degree rotations. And for the pair tensor Pab likewise Pab=Pba (1), and the delta function should be Pab too, instead.
One can introduce "gauges" and use an equivalent tensor formulation, using Pab for left and right turns, but (1) gets you into problems in no time and I never was able to find a "Lorentz-invariant" tensor set. The interesting solutions are even CPT-invariant (for intuitive interpretations of C, P, and T for abstract tensors, I even have charge and baryon number conservation automagically), but T(S)=S^-1 should hold (where I only can get T(S)=S for my solutions).
Am I doing something wrong or is Morse theory (or more precise, Kauffman's abstract tensor approach) symmetry-breaking by nature?