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An Invitation to Morse Theory

2011-12-02 Mathematics
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Release : 2011-12-02
Genre : Mathematics
Kind : eBook
Book Rating : 05X/5 ( reviews)

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Book Synopsis An Invitation to Morse Theory by : Liviu Nicolaescu

Download or read book An Invitation to Morse Theory written by Liviu Nicolaescu. This book was released on 2011-12-02. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Circle-valued Morse Theory

2006-01-01 Mathematics
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Release : 2006-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 979/5 ( reviews)

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Book Synopsis Circle-valued Morse Theory by : Andrei V. Pajitnov

Download or read book Circle-valued Morse Theory written by Andrei V. Pajitnov. This book was released on 2006-01-01. Available in PDF, EPUB and Kindle. Book excerpt: In 1927 M. Morse discovered that the number of critical points of a smooth function on a manifold is closely related to the topology of the manifold. This became a starting point of the Morse theory which is now one of the basic parts of differential topology. It is a large and actively developing domain of differential topology, with applications and connections to many geometrical problems. The aim of the present book is to give a systematic treatment of the geometric foundations of a subfield of that topic, the circle-valued Morse functions, a subfield of Morse theory.

Morse Theory: Smooth And Discrete

2015-05-29 Mathematics
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Release : 2015-05-29
Genre : Mathematics
Kind : eBook
Book Rating : 985/5 ( reviews)

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Book Synopsis Morse Theory: Smooth And Discrete by : Kevin P Knudson

Download or read book Morse Theory: Smooth And Discrete written by Kevin P Knudson. This book was released on 2015-05-29. Available in PDF, EPUB and Kindle. Book excerpt: Morse Theory: Smooth and Discrete serves as an introduction to classical smooth Morse theory and to Forman's discrete Morse theory, highlighting the parallels between the two subjects. This is the first time both smooth and discrete Morse theory have been treated in a single volume. This makes the book a valuable resource for students and professionals working in topology and discrete mathematics. With a strong focus on examples, the text is suitable for advanced undergraduates or beginning graduate students.

An Introduction to Morse Theory

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 224/5 ( reviews)

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Book Synopsis An Introduction to Morse Theory by : Yukio Matsumoto

Download or read book An Introduction to Morse Theory written by Yukio Matsumoto. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: Finite-dimensional Morse theory is easier to present fundamental ideas than in infinite-dimensional Morse theory, which is theoretically more involved. However, finite-dimensional Morse theory has its own significance. This volume explains the finte-dimensional Morse theory.

Lectures on Morse Homology

2013-03-09 Mathematics
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Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 96X/5 ( reviews)

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Book Synopsis Lectures on Morse Homology by : Augustin Banyaga

Download or read book Lectures on Morse Homology written by Augustin Banyaga. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a detailed presentation of results needed to prove the Morse Homology Theorem using classical techniques from algebraic topology and homotopy theory. The text presents results that were formerly scattered in the mathematical literature, in a single reference with complete and detailed proofs. The core material includes CW-complexes, Morse theory, hyperbolic dynamical systems (the Lamba-Lemma, the Stable/Unstable Manifold Theorem), transversality theory, the Morse-Smale-Witten boundary operator, and Conley index theory.

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