1.

Record Nr.

UNINA9910154749003321

Autore

Madsen Ib

Titolo

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

Pubbl/distr/stampa

Princeton, NJ : , : Princeton University Press, , [2016]

©1980

ISBN

1-4008-8147-1

Descrizione fisica

1 online resource (296 pages) : illustrations

Collana

Annals of Mathematics Studies ; ; 229

Disciplina

514/.223

Soggetti

Manifolds (Mathematics)

Classifying spaces

Surgery (Topology)

Cobordism theory

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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

Sommario/riassunto

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.