Universitext

An Invitation to Morse Theory

Authors: Nicolaescu, Liviu

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  • 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
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eBook $59.99
price for USA in USD (gross)
  • ISBN 978-1-4614-1105-5
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  • Immediate eBook download after purchase
Softcover $79.99
price for USA in USD
  • ISBN 978-1-4614-1104-8
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  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
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About this Textbook

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.

About the authors

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

Reviews

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 useful and 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)


Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-1-4614-1105-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA in USD
  • ISBN 978-1-4614-1104-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
An Invitation to Morse Theory
Authors
Series Title
Universitext
Copyright
2011
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4614-1105-5
DOI
10.1007/978-1-4614-1105-5
Softcover ISBN
978-1-4614-1104-8
Series ISSN
0172-5939
Edition Number
2
Number of Pages
XVI, 353
Number of Illustrations
47 b/w illustrations
Topics