Over the past few decades, Morse theory has undergone many generalizations, into many different fields.  At the moment, I only know of a few, and I understand even fewer. Well, let’s begin at the beginning: Classical Morse theory (CMT) Stratified Morse theory (SMT) Micro-local Morse theory (MMT) The core of these theories is, of course,

Stability and Genericity

Before I begin, I want to give credit where credit is due: much of the exposition (especially the proofs) of my last post was paraphrased from Guillemin and Pollack’s Differential Topology [1].  One of my favorites. Okay, moving on. We saw last time that Morse functions are pretty neat, and are abundant; “almost all” smooth functions