An Invitation to Morse TheorySpringer Science & Business Media, 9 août 2007 - 242 pages This book offers readers a taste of the "unreasonable effectiveness" of Morse theory. It covers many of the most important topics in Morse theory along with applications. The book details topics such as Morse-Smale flows, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. In addition, many examples, problems, and illustrations further enhance the value of this useful introduction to Morse Theory. |
Table des matières
| 1 | |
The Topology of Morse Functions | 23 |
Applications | 87 |
Basics of Complex Morse Theory | 151 |
Exercises and Solutions 193 | 192 |
| 233 | |
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Expressions et termes fréquents
action algebra associated assume boundary bundle called choose closed compact complex computations connected Consider consists containing coordinates Corollary corresponding critical points critical value cycle deduce defines Definition denote described determined diffeomorphism differential dimension dimensional disk embedded equality equivalent Example Exercise exists fact fiber Figure finite flow function f given Hamiltonian Hence homology hyperplane identified implies induced intersection invariant isomorphism knot Lefschetz Lemma linear metric morphism Morse function natural negligible neighborhood nondegenerate Note Observe obtain operator orientation pair particular path point of f polynomial positive precisely projective Proof prove refer Remark respect restriction result satisfying shows singular smooth function smooth manifold space sphere structure subset sufficiently Suppose surgery symplectic theorem theory topological torus transversally trivial vector field vector space