عنوان

Lusternik-Schnirelmann category /

0821834045 (alk. paper)

9780821834046 (alk. paper)

dltt

Lusternik-Schnirelmann category /

[Book]

Octav Cornea ... [et al.].

Providence, R.I. :

American Mathematical Society,

c2003.

xvii, 330 p. :

ill. ;

26 cm.

Mathematical surveys and monographs ;

v. 103

Includes bibliographical references (p. 311-324) and index.

1.3. The Lusternik-Schnirelmann Theorem 7 -- 1.4. Sums, Homotopy Invariance and Mapping Cones 13 -- 1.5. Products and Fibrations 17 -- 1.6. The Whitehead and Ganea Formulations of Category 22 -- 1.7. Axioms and Category 33 -- Chapter 2. Lower Bounds for LS-Category 47 -- 2.2. Ganea Fibrations of a Product 49 -- 2.3. Toomer's Invariant 52 -- 2.4. Weak Category 55 -- 2.5. Conilpotency of a Suspension 57 -- 2.6. Suspension of the Category 60 -- 2.7. Category Weight 62 -- 2.8. Comparison Theorem 66 -- Chapter 3. Upper Bounds for Category 75 -- 3.2. First Properties of Upper Bounds 76 -- 3.3. Geometric Category is not a Homotopy Invariant 79 -- 3.4. Strong Category and Category Differ by at Most One 82 -- 3.5. Cone-length 83 -- 3.6. Stabilization of Ball Category 92 -- 3.7. Constraints Implying Equality of Category and Upper Bounds 98 -- Chapter 4. Localization and Category 105 -- 4.2. Localization of Groups and Spaces 106 -- 4.3. Localization and Category 111 -- 4.4. Category and the Mislin Genus 114 -- 4.5. Fibrewise Construction 120 -- 4.6. Fibrewise Construction and Category 121 -- 4.7. Examples of Fibrewise Construction 123 -- Chapter 5. Rational Homotopy and Category 129 -- 5.2. Rational Homotopy Theory 130 -- 5.3. Rational Category and Minimal Models 137 -- 5.4. Rational Category and Fibrations, Including Products 144 -- 5.5. Lower and Upper Bounds in the Rational Context 153 -- 5.6. Geometric Version of mcat 158 -- Chapter 6. Hopf Invariants 165 -- 6.2. Hopf Invariants of Maps S[superscript r] to S[superscript n] 167 -- 6.3. The Berstein-Hilton Definition 172 -- 6.4. Hopf Invariants and LS-category 176 -- 6.5. Crude Hopf Invariants 180 -- 6.7. Hopf-Ganea Invariants 188 -- 6.8. Iwase's Counterexamples to the Ganea Conjecture 192 -- 6.9. Fibrewise Construction and Hopf Invariants 195 -- Chapter 7. Category and Critical Points 203 -- 7.2. Relative Category 204 -- 7.3. Local Study of Isolated Critical Points 208 -- 7.4. Functions with Few Critical Points: the Stable Case 213 -- 7.5. Closed Manifolds 217 -- 7.6. Fusion of Critical Points and Hopf Invariants 221 -- 7.7. Functions Quadratic at Infinity 225 -- Chapter 8. Category and Symplectic Topology 233 -- 8.2. The Arnold Conjecture 233 -- 8.3. Manifolds with [omega vertical bar superscript pi 2M] = 0 and Category Weight 240 -- 8.4. The Arnold Conjecture for Symplectically Aspherical Manifolds 244 -- 8.5. Other Symplectic Connections 245 -- Chapter 9. Examples, Computations and Extensions 253 -- 9.2. Category and the Free Loop Space 253 -- 9.3. Sectional Category 259 -- 9.4. Category and the Complexity of Algorithms 263 -- 9.5. Category and Group Actions 267 -- 9.6. Category of Lie Groups 273 -- 9.7. Category and 3-Manifolds 279 -- 9.8. Other Developments 282 -- Appendix A. Topology and Analysis 287 -- A.1. Types of Spaces 287 -- A.2. Morse Theory 289 -- Appendix B. Basic Homotopy 293 -- B.1. Whitehead's Theorem 293 -- B.2. Homotopy Pushouts and Pullbacks 293 -- B.3. Cofibrations 295 -- B.4. Fibrations 298 -- B.5. Mixing Cofibrations and Fibrations 301 -- B.6. Properties of Homotopy Pushouts 301 -- B.7. Properties of Homotopy Pullbacks 302 -- B.8. Mixing Homotopy Pushouts and Homotopy Pullbacks 303 -- B.9. Homotopy Limits and Colimits 306.

0

Algebraic topology.

Lusternik-Schnirelmann category.

Cornea, O., (Octavian),1966-

20140219125525.0

[Book]

Y