Lectures on Morse Homology
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BeschreibungThis book presents in great detail all the results one needs to prove the Morse Homology Theorem using classical techniques from algebraic topology and homotopy theory. Most of these results can be found scattered throughout the literature dating from the mid to late 1900's in some form or other, but often the results are proved in different contexts with a multitude of different notations and different goals. This book collects all these results together into a single reference with complete and detailed proofs.The core material in this book 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. More advanced topics include Morse theory on Grassmann manifolds and Lie groups, and an overview of Floer homology theories. With the stress on completeness and by its elementary approach to Morse homology, this book is suitable as a textbook for a graduate level course, or as a reference for working mathematicians and physicists.
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.
PressestimmenFrom the reviews of the first edition:
"This book presents in great detail all the results one needs to prove the Morse homology theorem using classical techniques from algebraic topology and homotopy theory. ... This book collects all these results together into a single reference with complete and detailed proofs. ... With the stress on completeness and by its elementary approach to Morse homology, this book is suitable as a textbook for a graduate level course, or as a reference for working mathematicians and physicists." (Bulletin Bibliographique, Vol. 51 (1-2), 2005)
"This book provides a treatment of finite-dimensional Morse theory and its associated chain complex, pitched at a level appropriate to early-stage graduate students. ... Throughout, the authors take pains to make the material accessible, and ... extensive references are provided. ... Many well-drawn figures are provided to clarify the text, and there are over 200 exercises, with hints for some of them in the back. ... Banyaga and Hurtubise's book provides a valuable service by introducing young mathematicians to a circle of ideas ... ." (Michael J. Usher, Mathematical Reviews, Issue 2006 i)
"This book is an exposition of the 'classical' approach to finite dimensional Morse homology. ... This book presents in great detail all the results one needs to prove the Morse Homology theorem ... . References to the literature are provided throughout the book ... . A lot of examples, suggestive figures and diagrams in every chapter and many useful exercises at the end of the chapters makes this book a good and attractive textbook (as well as an excellent monograph). ... The bibliography is exhaustive." (Ioan Pop, Zentralblatt MATH, Vol. 1080, 2006)
Untertitel: 2004. Auflage. Book. Sprache: Englisch.
Erscheinungsdatum: Oktober 2004
Seitenanzahl: 340 Seiten