| Preface | p. xi |
| Introduction to LS-Category | p. 1 |
| Introduction | p. 1 |
| The Definition and Basic Properties | p. 1 |
| The Lusternik-Schnirelmann Theorem | p. 7 |
| Sums, Homotopy Invariance and Mapping Cones | p. 13 |
| Products and Fibrations | p. 17 |
| The Whitehead and Ganea Formulations of Category | p. 22 |
| Axioms and Category | p. 33 |
| Exercises for Chapter 1 | p. 40 |
| Lower Bounds for LS-Category | p. 47 |
| Introduction | p. 47 |
| Ganea Fibrations of a Product | p. 49 |
| Toomer's Invariant | p. 52 |
| Weak Category | p. 55 |
| Conilpotency of a Suspension | p. 57 |
| Suspension of the Category | p. 60 |
| Category Weight | p. 62 |
| Comparison Theorem | p. 66 |
| Examples | p. 70 |
| Exercises for Chapter 2 | p. 71 |
| Upper Bounds for Category | p. 75 |
| Introduction | p. 75 |
| First Properties of Upper Bounds | p. 76 |
| Geometric Category is not a Homotopy Invariant | p. 79 |
| Strong Category and Category Differ by at Most One | p. 82 |
| Cone-length | p. 83 |
| Stabilization of Ball Category | p. 92 |
| Constraints Implying Equality of Category and Upper Bounds | p. 98 |
| Exercises for Chapter 3 | p. 101 |
| Localization and Category | p. 105 |
| Introduction | p. 105 |
| Localization of Groups and Spaces | p. 106 |
| Localization and Category | p. 111 |
| Category and the Mislin Genus | p. 114 |
| Fibrewise Construction | p. 120 |
| Fibrewise Construction and Category | p. 121 |
| Examples of Fibrewise Construction | p. 123 |
| Exercises for Chapter 4 | p. 125 |
| Rational Homotopy and Category | p. 129 |
| Introduction | p. 129 |
| Rational Homotopy Theory | p. 130 |
| Rational Category and Minimal Models | p. 137 |
| Rational Category and Fibrations, Including Products | p. 144 |
| Lower and Upper Bounds in the Rational Context | p. 153 |
| Geometric Version of mcat | p. 158 |
| Exercises for Chapter 5 | p. 161 |
| Hopf Invariants | p. 165 |
| Introduction | p. 165 |
| Hopf Invariants of Maps S[superscript r] to S[superscript n] | p. 167 |
| The Berstein-Hilton Definition | p. 172 |
| Hopf Invariants and LS-category | p. 176 |
| Crude Hopf Invariants | p. 180 |
| Examples | p. 184 |
| Hopf-Ganea Invariants | p. 188 |
| Iwase's Counterexamples to the Ganea Conjecture | p. 192 |
| Fibrewise Construction and Hopf Invariants | p. 195 |
| Exercises for Chapter 6 | p. 199 |
| Category and Critical Points | p. 203 |
| Introduction | p. 203 |
| Relative Category | p. 204 |
| Local Study of Isolated Critical Points | p. 208 |
| Functions with Few Critical Points: the Stable Case | p. 213 |
| Closed Manifolds | p. 217 |
| Fusion of Critical Points and Hopf Invariants | p. 221 |
| Functions Quadratic at Infinity | p. 225 |
| Exercises for Chapter 7 | p. 231 |
| Category and Symplectic Topology | p. 233 |
| Introduction | p. 233 |
| The Arnold Conjecture | p. 233 |
| Manifolds with [omega vertical bar superscript pi 2M] = 0 and Category Weight | p. 240 |
| The Arnold Conjecture for Symplectically Aspherical Manifolds | p. 244 |
| Other Symplectic Connections | p. 245 |
| Exercises for Chapter 8 | p. 251 |
| Examples, Computations and Extensions | p. 253 |
| Introduction | p. 253 |
| Category and the Free Loop Space | p. 253 |
| Sectional Category | p. 259 |
| Category and the Complexity of Algorithms | p. 263 |
| Category and Group Actions | p. 267 |
| Category of Lie Groups | p. 273 |
| Category and 3-Manifolds | p. 279 |
| Other Developments | p. 282 |
| Exercises for Chapter 9 | p. 283 |
| Topology and Analysis | p. 287 |
| Types of Spaces | p. 287 |
| Morse Theory | p. 289 |
| Basic Homotopy | p. 293 |
| Whitehead's Theorem | p. 293 |
| Homotopy Pushouts and Pullbacks | p. 293 |
| Cofibrations | p. 295 |
| Fibrations | p. 298 |
| Mixing Cofibrations and Fibrations | p. 301 |
| Properties of Homotopy Pushouts | p. 301 |
| Properties of Homotopy Pullbacks | p. 302 |
| Mixing Homotopy Pushouts and Homotopy Pullbacks | p. 303 |
| Homotopy Limits and Colimits | p. 306 |
| Bibliography | p. 311 |
| Index | p. 325 |
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