Lusternik-Schnirelmann CategoryAmerican Mathematical Soc., 2003 - 330 pages ''Lusternik-Schnirelmann category is like a Picasso painting. Looking at category from different perspectives produces completely different impressions of category's beauty and applicability.'' --from the Introduction Lusternik-Schnirelmann category is a subject with ties to both algebraic topology and dynamical systems. The authors take LS-category as the central theme, and then develop topics in topology and dynamics around it. Included are exercises and many examples. The book presents the material in a rich, expository style. The book provides a unified approach to LS-category, including foundational material on homotopy theoretic aspects, the Lusternik-Schnirelmann theorem on critical points, and more advanced topics such as Hopf invariants, the construction of functions with few critical points, connections with symplectic geometry, the complexity of algorithms, and category of $3$-manifolds. This is the first book to synthesize these topics. It takes readers from the very basics of the subject to the state of the art. Prerequisites are few: two semesters of algebraic topology and, perhaps, differential topology. It is suitable for graduate students and researchers interested |
Table des matières
| xix | |
Chapter 2 Lower Bounds for LSCategory | 47 |
Chapter 3 Upper Bounds for Category | 75 |
Chapter 4 Localization and Category | 105 |
Chapter 5 Rational Homotopy and Category | 129 |
Chapter 6 Hopf Invariants | 165 |
Chapter 7 Category and Critical Points | 203 |
Chapter 8 Category and Symplectic Topology | 233 |
Chapter 9 Examples Computations and Extensions | 253 |
Appendix A Topology and Analysis | 287 |
Appendix B Basic Homotopy | 293 |
| 311 | |
| 325 | |
Expressions et termes fréquents
algebra Arnold conjecture ballcat basepoint cat(f cat(M cat(S cat(X cat(Y categorical cover category weight cato Chapter closed manifold cofibration cofibration sequence commutative diagram compact consider construction contractible Corollary Crit(M critical points CW-complex defined denote DG-algebra diagonal diffeomorphism dim(M dimension example Exercise exists finite type flow functor Ganea conjecture Ganea fibration Gn(X Hamiltonian Hence homeomorphic homotopy commutative homotopy equivalence homotopy fibre homotopy pullback homotopy pushout homotopy type Hopf invariant inclusion induced inequality injection isomorphism Lemma Let f lower bound LS-category manifold map f minimal model Morse nilpotency non-degenerate number of critical obtain open sets orbit P-localization path-connected Poincaré duality prime proof of Theorem prove Qcat quasi-isomorphism rational homotopy Recall REMARK result satisfies simply connected space smooth sphere strong category Suppose surjective suspension symplectic symplectic manifold Toomer invariant topological trivial weat(X wedge