what is level curves? what is non-critical level curves?

differential-geometry riemannian-geometry morse-theory mapping-class-group

The classic example of a Morse function is the height on an upright torus. In the diagram, the torus is cut off at the bottom, creating a boundary curve in red; the three critical levels (the two figure-8 curves and the point at top) are blue, typical non-critical levels are green, and the associated graph is at right.

The graph associated to a Morse function

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