Classifying Spaces for Surgery and Corbordism of Manifolds. (AM-92), Volume 92 / R. James Milgram, Ib Madsen.

Format:

Book

Author/Creator:

Madsen, Ib, author.

Milgram, R. James, author.

Series:

Annals of mathematics studies ; Number 92.

Annals of Mathematics Studies ; 229

Language:

English

Subjects (All):

Manifolds (Mathematics).

Classifying spaces.

Surgery (Topology).

Cobordism theory.

Physical Description:

1 online resource (296 pages) : illustrations.

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

English

Summary:

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.

Contents:

Frontmatter

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[½] AND MSTOP[½]

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

Backmatter

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781400881475

1400881471

OCLC:

979911330