Lectures on Morse Homology
著者
書誌事項
Lectures on Morse Homology
（Kluwer texts in the mathematical sciences, 29）
Springer Science+Business Media, [2011?], c2004
- : softcover
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注記
"A graduate-level book series"--P. facing t.p
"Originally published by Kluwer Academic Publishers in 2004. Softcover reprint of the hardcover 1st edition 2004"--T.p. verso
"Based on the lecture notes from a course we taught at Penn State University during the fall of 2002"--Pref
Includes bibliographical references (p. [309]-315) and indexes
内容説明・目次
内容説明
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.
目次
1. Introduction.- 2. The CW-Homology Theorem.- 3. Basic Morse Theory.- 4. The Stable/Unstable Manifold Theorem.- 5. Basic Differential Topology.- 6. Morse-Smale Functions.- 7. The Morse Homology Theorem.- 8. Morse Theory On Grassmann Manifolds.- 9. An Overview of Floer Homology Theories.- Hints and References for Selected Problems.- Symbol Index.
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