这本《莫尔斯理论入门》由美国的Liviu Nicolaescu所著，内容是：The present book is divided into three conceptually distinct parts. In thefirst part we lay the foundations of Morse theory (over the reals). The secondpart consists of applications of Morse theory over the reals, while the lastpart describes the basics and some applications of complex Morse theory,a.k.a. Picard-Lefschetz theory. Here is a more detailed presentation of thecontents.

Preface

Notations and conventions

1  Morse Functions

1.1 The Local Structure of Morse Functions

1.2 Existence of Morse Functions

2  The Topology of Morse Functions

2.1 Surgery, Handle Attachment, and Cobordisms

2.2 The Topology of Sublevel Sets

2.3 Morse Inequalities

2.4 Morse-Smale Dynamics

2.5 Morse-Floer Homology

2.6 Morse-Bott Functions

2.7 Min-Max Theory

3  Applications

3.1 The Cohomology of Complex Grassmannians

3.2 Lefschetz Hyperplane Theorem

3.3 Symplectic Manifolds and Hamiltonian Flows

3.4 Morse Theory of Moment Maps

3.5 S1-Equivariant Localization

4  Basics of Complex Morse Theory

4.1 Some Fundamental Constructions

4.2 Topological Applications of Lefschetz Pencils

4.3 The Hard Lefschetz Theorem

4.4 Vanishing Cycles and Local Monodromy

4.5 Proof of the Picard-Lefschetz formula

4.6 Global Picard-Lefschetz Formulae

5  Exercises and Solutions

5.1 Exercises

5.2 Solutions to Selected Exercises

References

Index