ABSTRACT
Chapter 2
The Topology of Foliations
on Two-Dimensional Surfaces
Generated by Morse Functions
2.1. SIMPLE MORSE FUNCTIONS
Consider the space of smooth functions on a smooth manifold. What is the structure
of typical smooth functions that are in some sense generic? How do they
dier from \exotic" functions? It is clear that the properties of a function
are determined mostly by the character of its singularities, i.e., those points where
the dierential of the function vanishes. That is why we can reduce the above
question to the question about functions with typical singularities.
