An Invitation to Morse Theory

This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology, and will also be of interest to researchers. This is the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. Some features of the second edition include added applications, such as Morse theory and the curvature of knots, the cohomology of the moduli space of planar polygons, and the Duistermaat-Heckman formula. The second edition also includes a new chapter on Morse-Smale flows and Whitney stratifications, many new exercises, and various corrections from the first edition.

New edition extensively revised and updated with three new applications and a new chapter on Morse-Smale flows and Whitney stratifications Provides a useful introduction to Morse Theory Covers many of the most important topics in Morse theory along with a broad range of applications Contains many excellent exercises Far more up-to-date and less specialized than any other book on Morse Theory Includes supplementary material: sn.pub/extras

Autorentext

Liviu Nicolaescu is currently Professor of Mathematics at the University of Notre Dame.

Inhalt
Preface.- Notations and Conventions.- 1 Morse Functions.- 2 The Topology of Morse Functions.- 3 Applications.- 4 Morse-Smale Flows and Whitney Stratifications.- 5 Basics of Complex Morse Theory.- 6 Exercises and Solutions.- References.- Index