05476nam 22013695 450 991015474900332120190708092533.01-4008-8147-110.1515/9781400881475(CKB)3710000000627293(SSID)ssj0001651249(PQKBManifestationID)16426233(PQKBTitleCode)TC0001651249(PQKBWorkID)14013790(PQKB)10618393(MiAaPQ)EBC4738510(DE-B1597)468012(OCoLC)979911330(DE-B1597)9781400881475(EXLCZ)99371000000062729320190708d2016 fg engurcnu||||||||txtccrClassifying Spaces for Surgery and Corbordism of Manifolds. (AM-92), Volume 92 /R. James Milgram, Ib MadsenPrinceton, NJ : Princeton University Press, [2016]©19801 online resource (296 pages) illustrationsAnnals of Mathematics Studies ;229Bibliographic Level Mode of Issuance: Monograph0-691-08225-1 0-691-08226-X Includes bibliographical references and index.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 -- BackmatterBeginning 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.Annals of mathematics studies ;Number 92.Manifolds (Mathematics)Classifying spacesSurgery (Topology)Cobordism theoryBijection.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.Manifolds (Mathematics)Classifying spaces.Surgery (Topology)Cobordism theory.514/.223Madsen Ib, 55804Milgram R. James, DE-B1597DE-B1597BOOK9910154749003321Classifying Spaces for Surgery and Corbordism of Manifolds. (AM-92), Volume 922788679UNINA