ABSTRACT
Morse theory can be viewed as a generalized version of the local maxima and minima tests from calculus: for a 1-variable function, the points where the graph changes most dramatically — the minimum and maximum points — are among the critical points of the function. This principle, translated to the setting of Morse theory, says that, for a generic real-valued function on a manifold, the changes in the topology of the level sets occur at the critical points of the function.
