Liviu Nicolaescu

An Invitation to Morse Theory (eBook, PDF)

• Format: PDF

Produktbeschreibung

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. The reader is expected to have some familiarity with cohomology theory and 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.

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Produktdetails

• Verlag: Springer-Verlag GmbH
• Seitenzahl: 353
• Erscheinungstermin: 2. Dezember 2011
• Englisch
• ISBN-13: 9781461411055
• Artikelnr.: 37346367

Autorenporträt

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

Inhaltsangabe

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

Rezensionen

From the reviews:

"Morse theory, a tool within differential topology, strategically studies a given abstract smooth manifold by first imposing on it a nearly arbitrary numerical function, and then cleverly extracting from it purely topological information. ... Undergraduates will see that the foundations of this advanced topic build directly on a(n honest) course in multivariable calculus ... . Primarily for mathematics students. Summing Up: Recommended. Upper-division undergraduates through professionals." (D. V. Feldman, CHOICE, Vol. 45 (6), February, 2008)

"The book is a nicely written self-contained introduction to Morse theory ... will be useful for mathematicians of various levels, including graduate students and researchers." (Michael Farber, Zentralblatt MATH, Vol. 1131, 2008)

"Nicolaescu's book starts with the basics of Morse theory over the reals ... . The discussion continuously presents some really nice and well chosen applications of the theory, and finally lets the reader see, that the whole theory can go on to complex, where the set of regular values, that is disconnected by nature over the reals, becomes connected. ... This book is warmly recommended for interested graduate students and researcher ... ." (Árpád Kurusa, Acta Scientiarum Mathematicarum, Vol. 74, 2008)

"Nicolaescu's book complements previous books on Morse theory by quickly developing the foundations of the subject in terms of gradient-like vector fields and discussing applications not found in other books on Morse theory. ... the book is recommended for graduate students and researchers ... ." (David E. Hurtubise, Mathematical Reviews, Issue 2009 m)

From the reviews of the second edition:

"The present book provides a wonderful presentation of concepts and ideas as well as problems with their solutions in Morse Theory, an important and challenging part of Differential Topology. ... The book ends with an usefuland relevant bibliography containing 85 references. It also contains an index of symbols and a subject index. ... 'The book will be useful for mathematicians of various levels, including graduate students and researchers'." (Dorin Andrica, Zentralblatt MATH, Vol. 1238, 2012)