An Invitation to Morse Theory

  • LiviuĀ Nicolaescu

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Pages 1-22
  3. Pages 87-150
  4. Pages 193-232
  5. Back Matter
    Pages 233-241

About this book


This self-contained treatment of Morse Theory focuses on applications and is intended for a graduate course on differential or algebraic topology. The book is divided into three conceptually distinct parts. The first part contains the foundations of Morse theory (over the reals). The second part consists of applications of Morse theory over the reals, while the last part describes the basics and some applications of complex Morse theory, a.k.a. Picard-Lefschetz theory.

This is the first textbook to include topics such as Morse-Smale flows, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The exposition is enhanced with examples, problems, and illustrations, and will be of interest to graduate students as well as researchers. The reader is expected to have some familiarity with cohomology theory and with the differential and integral calculus on smooth manifolds.

Liviu Nicolaescu is Associate Professor of Mathematics at University of Notre Dame.


Algebraic topology Topology algebra calculus cohomology cohomology theory function homology manifold mathematics

Authors and affiliations

  • LiviuĀ Nicolaescu
    • 1
  1. 1.Mathematics DepartmentUniversity of Notre DameNotre DameUSA

Bibliographic information