Chapter 4. Homotopy Theory

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• 4.1. Homotopy Groups
  • Definitions and Basic Constructions
  • Whitehead’s Theorem
  • Cellular Approximation
  • CW Approximation
• 4.2. Elementary Methods of Calculation
  • Excision for Homotopy Groups
  • The Hurewicz Theorem
  • Fiber Bundles
  • Stable Homotopy Groups
• 4.3. Connections with Cohomology
  • The Homotopy Construction of Cohomology
  • Fibrations
  • Postnikov Towers
  • Obstruction Theory
• Additional Topics
  • 4.A. Basepoints and Homotopy
  • 4.B. The Hopf Invariant
  • 4.C. Minimal Cell Structures
  • 4.D. Cohomology of Fiber Bundles
  • 4.E. The Brown Representability Theorem
  • 4.F. Spectra and Homology Theories
  • 4.G. Gluing Constructions
  • 4.H. Eckmann-Hilton Duality
  • 4.I. Stable Splittings of Spaces
  • 4.J. The Loopspace of a Suspension
  • 4.K. The Dold-Thom Theorem
  • 4.L. Steenrod Squares and Powers