Algebraic L̲-theory and topological manifolds
著者
書誌事項
Algebraic L̲-theory and topological manifolds
（Cambridge tracts in mathematics, 102）
Cambridge University Press, 1992
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注記
Bibliography: p. 343-353
Includes index
内容説明・目次
内容説明
This book presents a definitive account of the applications of the algebraic L-theory to the surgery classification of topological manifolds. The central result is the identification of a manifold structure in the homotopy type of a Poincare duality space with a local quadratic structure in the chain homotopy type of the universal cover. The difference between the homotopy types of manifolds and Poincare duality spaces is identified with the fibre of the algebraic L-theory assembly map, which passes from local to global quadratic duality structures on chain complexes. The algebraic L-theory assembly map is used to give a purely algebraic formulation of the Novikov conjectures on the homotopy invariance of the higher signatures; any other formulation necessarily factors through this one. The book is designed as an introduction to the subject, accessible to graduate students in topology; no previous acquaintance with surgery theory is assumed, and every algebraic concept is justified by its occurrence in topology.
目次
- Introduction
- Summary
- Part I. Algebra: 1. Algebraic Poincare complexes
- 2. Algebraic normal complexes
- 3. Algebraic bordism categories
- 4. Categories over complexes
- 5. Duality
- 6. Simply connected assembly
- 7. Derived product and Hom
- 8. Local Poincare duality
- 9. Universal assembly
- 10. The algebraic - theorem
- 11. -sets
- 12. Generalized homology theory
- 13. Algebraic L-spectra
- 14. The algebraic surgery exact sequence
- 15. Connective L-theory
- Part II. Topology: 16. The L-theory orientation of topology
- 17. The total surgery obstruction
- 18. The structure set
- 19. Geometric Poincare complexes
- 20. The simply connected case
- 21. Transfer
- 22. Finite fundamental group
- 23. Splitting
- 24. Higher signatures
- 25. The 4-periodic theory
- 26. Surgery with coefficients
- Appendices
- Bibliography
- Index.
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