An Invitation to Morse Theory
Seiten
2011
|
2nd ed. 2011
Springer-Verlag New York Inc.
978-1-4614-1104-8 (ISBN)
Springer-Verlag New York Inc.
978-1-4614-1104-8 (ISBN)
This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology. 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.
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. 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, Floer homology, 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.
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.
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. 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, Floer homology, 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.
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.
Liviu Nicolaescu is currently Professor of Mathematics at the University of Notre Dame.
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
| Reihe/Serie | Universitext |
|---|---|
| Zusatzinfo | 47 Illustrations, black and white; XVI, 353 p. 47 illus. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Schlagworte | Morse functions • Morsesche Theorie • Morse-Smale flows • Picard-Lefschetz theory • Surgery • Whitney stratifications |
| ISBN-10 | 1-4614-1104-1 / 1461411041 |
| ISBN-13 | 978-1-4614-1104-8 / 9781461411048 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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