Screen LibraryAn invitation to Morse theory
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| Main Authors: | |
|---|---|
| Published: |
Springer,
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| Publisher Address: | New York London |
| Publication Dates: | 2007. |
| Literature type: | Book |
| Language: | English |
| Series: |
Universitext |
| Subjects: | |
| Carrier Form: | xiv, 241 p.: ; 24 cm. |
| ISBN: |
9780387495095 (pbk.) 0387495096 (pbk.) 038749510X (ebk.) 9780387495101 (ebk.) |
| Index Number: | O189 |
| CLC: | O189 |
| Call Number: | O189/N634 |
| Contents: |
Includes bibliographical references (p. [233]-235) and index. Notations and conventions -- 1. Morse functions -- The local structure of Morse functions -- Existence of Morse functions -- 2. The topology of Morse functions -- Surgery, handle attachment, and cobordisms -- The topology of sublevel sets -- Morse inequalities -- Morse-Smale dynamics -- Morse-Floer homology -- Morse-Bott functions -- Min-Max theory -- 3. Applications -- The cohomology of complex grassmannians -- Lefschetz hyderplane theorem -- Symplectic manifolds and Hamiltonian flows -- Morse theory of moment maps -- S¹-Equivariant localization -- 4. Basics of complex Morse theory -- Some fundamental constructions -- Topological applications of Lefschetz pencils -- The hard Lefschetz theorem -- Vanishing cycles and local monodromy -- Proof of the Picard-Lefschetz formulæ -- 5. Exercises and solutions -- Exercises -- Solutions to selected exercises. |