The Topology of Morse Functions

Part of the Universitext book series (UTX)


The present chapter is the heart of Morse theory, which is based on two fundamental principles. The “weak” Morse principle states that as long as the real parameter t varies in an interval containing only regular values of a smooth function f: M → ℝ, then the topology of the sublevel set ft is independent of t. We can turn this on its head and state that a change in the topology of ft is an indicator of the presence of a critical point.


Unstable Manifold Smooth Manifold Normal Bundle Morse Function Solid Torus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media, Inc. 2007

Personalised recommendations