title: The Topology of Fibre Bundles. (PMS-14)
author: Norman Steenrod
description: <b>Norman Steenrod</b> was a professor of Mathematics at Princeton University and a member of the National Academy Of Sciences. He also edited <i>Reviews in Topology.</i>
zlib_text: 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  Version 1.3, July 2001
  
  
  **Allen Hatcher**
  
  
  Copyright c
  
  
  2001 by Allen Hatcher
  
  
  Paper or electronic copies for noncommercial use may be made freely without
  explicit permission from the author.
  
  
  All other rights reserved.
  
  
  **Table of Contents**
  
  
  **Chapter 1. Vector Bundles**
  
  
  **1.1. Basic Definitions and Constructions**
  
  
  . . . . . . . . . . . . 1
  
  
  Sections 3. Direct Sums 5. Pullback Bundles 5. Inner Products 7.
  
  
  Subbundles 8. Tensor Products 9. Associated Bundles 11.
  
  
  **1.2. Classifying Vector Bundles**. . . . . . . . . . . . . . . . .
  
  
  12
  
  
  The Universal Bundle 12. Vector Bundles over Spheres 16.
  
  
  Orientable Vector Bundles 21. A Cell Structure on Grassmann Manifolds 22.
  
  
  Appendix: Paracompactness 24.
  
  
  **Chapter 2. Complex K-Theory**
  
  
  **2.1. The Functor K(X)**
  
  
  . . . . . . . . . . . . . . . . . . . . . . .
  
  
  28
  
  
  Ring Structure 31. Cohomological Properties 32.
  
  
  **2.2. Bott Periodicity**
  
  
  . . . . . . . . . . . . . . . . . . . . . . . .
  
  
  38
  
  
  Clutchin