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 PoincarC) duality space with a local quadratic structure in the chain homotopytype of the universal cover. The difference between the homotopy types of manifolds and PoincarC) duality spaces is identified with the fibre of the algebraic L-theory assembly map, which passes from local to global quadratic dualitystructures on chain complexes. The algebraic L-theory assembly map is used togive 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. INDICE: Introduction; Summary; Part I. Algebra: 1. Algebraic PoincarC) 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 PoincarC) duality; 9. Universal assembly; 10. The algebraic O-O theorem; 11. b-sets; 12. Generalized homology theory; 13. AlgebraicL-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 PoincarC) 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; Indexk
- ISBN: 978-0-521-05521-5
- Editorial: Cambridge University
- Encuadernacion: Rústica
- Páginas: 368
- Fecha Publicación: 20/03/2008
- Nº Volúmenes: 1
- Idioma: Inglés
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