I am a PhD student. I work on transversal submanifolds. I want to know if someone has an example of application of transversality in physics or engineering or in any other area. I hear that there is an application in the construction of plans but I didn't find it.
The key point of transversality is that it is stable. A transverse intersection persists under perturbations. Moreover: any intersection can be perturbed to be transverse. Moreover: almost any perturbation will do this!
Measurements are never precise: They are always perturbations of the real state. When I say "real state" I mean this in the classical sense, I am not talking about quantum mechanics here.
That means that our measurements will always measure transverse states. You cannot measure any non-transverse situation! Transversality is the only thing we observe!