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

• Autore: Madsen Ib
• Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2016]; ©1980
• Descrizione fisica: 1 online resource (296 pages) : illustrations
• Disciplina: 514/.223
• Soggetto topico: Manifolds (Mathematics); Classifying spaces; Surgery (Topology); Cobordism theory
• Soggetto non controllato: Bijection; Calculation; Characteristic class; Classification theorem; Classifying space; Closed manifold; Cobordism; Coefficient; Cohomology; Commutative diagram; Commutative property; Complex projective space; Connected sum; Corollary; Cup product; Diagram (category theory); Differentiable manifold; Disjoint union; Disk (mathematics); Effective method; Eilenberg–Moore spectral sequence; Elaboration; Equivalence class; Exact sequence; Exterior algebra; Fiber bundle; Fibration; Function composition; H-space; Homeomorphism; Homomorphism; Homotopy fiber; Homotopy group; Homotopy; Hopf algebra; Iterative method; Loop space; Manifold; Massey product; N-sphere; Normal bundle; Obstruction theory; Pairing; Permutation; Piecewise linear manifold; Piecewise linear; Polynomial; Prime number; Projective space; Sequence; Simply connected space; Special case; Spin structure; Steenrod algebra; Subset; Summation; Tensor product; Theorem; Topological group; Topological manifold; Topology; Total order
• Persona (resp. second.): MilgramR. James
• 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.
• Titolo autorizzato: Classifying Spaces for Surgery and Corbordism of Manifolds. (AM-92), Volume 92
• ISBN: 1-4008-8147-1
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910154749003321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; Number 92.