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The Topology of Morse Functions

  • Liviu NicolaescuEmail author
Chapter
Part of the Universitext book series (UTX)

Abstract

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 \(f : M \rightarrow \mathbb{R}\), the topology of the sublevel set {f ≤ t} is independent of t. We can turn this on its head and state that a change in the topology of {f ≤ t} is an indicator of the presence of a critical point.

Keywords

Vector Bundle Smooth Manifold Normal Bundle Morse Theory Morse Function 
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.

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Notre DameNotre DameUSA

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