Classifying Spaces for Surgery and Corbordism of Manifolds

Ib Madsen, R. James Milgram

• Publisher: Princeton University Press
• Year: 2016
• Print ISBN:
  9780691082264
  9780691082257
• eBook ISBN:
  9781400881475
• Topic: Mathematics
• Subtopic: Geometry
• Index: Mathematics

Beginning with a general discussion of bordism, Professors Madsen and Milgram present the homotopy theory of the surgery classifying spaces and the classifying spaces for the various required bundle theories. The next part covers more recent work on the maps between these spaces and the properties of the PL and Top characteristic classes, and includes integrality theorems for topological and PL manifolds. Later chapters treat the integral cohomology of BPL and Btop. The authors conclude with a discussion of the PL and topological cobordism rings and a construction of the torsion-free generators.

Table of contents

• Cover
• Title
• Copyright
• CONTENTS
• INTRODUCTION
• CHAPTER 1. CLASSIFYING SPACES AND COBORDISM
• CHAPTER 2. THE SURGERY CLASSIFICATION OF MANIFOLDS
• CHAPTER 3. THE SPACES SG AND BSG
• CHAPTER 4. THE HOMOTOPY STRUCTURE OF G/PL AND G/TOP
• CHAPTER 5. THE HOMOTOPY STRUCTURE OF MSPL[1/2] AND MSTOP[1/2]
• CHAPTER 6. INFINITE LOOP SPACES AND THEIR HOMOLOGY OPERATIONS
• CHAPTER 7. THE 2-LOCAL STRUCTURE OF B(G/TOP)
• CHAPTER 8. THE TORSION FREE STRUCTURE OF THE ORIENTED COBORDISM RINGS
• CHAPTER 9. THE TORSION FREE COHOMOLOGY OF G/TOP AND G/PL
• CHAPTER 10. THE TORSION FREE COHOMOLOGY OF BTOP AND BPL
• CHAPTER 11. INTEGRALITY THEOREMS
• CHAPTER 12. THE SMOOTH SURGERY CLASSES AND H*(BTOP; Z/2)
• CHAPTER 13. THE BOCKSTEIN SPECTRAL SEQUENCE FOR BTOP
• CHAPTER 14. THE TYPES OF TORSION GENERATORS
• APPENDIX. THE PROOFS OF 13.12, 13.13, AND 13.15
• BIBLIOGRAPHY
• INDEX