## 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.