Algebraic L-Theory and Topological Manifolds

Klappentext This book explains the applications of quadratic forms to the classification of topological manifolds! in a unified algebraic framework. Zusammenfassung 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 Poincaré duality space with a local quadratic structure in the chain homotopy type of the universal cover. Inhaltsverzeichnis Introduction; Summary; Part I. Algebra: 1. Algebraic Poincaré 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 Poincaré 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 Poincaré 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.

Product details

• Authors: A. A. Ranicki, A. A. (University of Edinburgh) Ranicki
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Paperback / Softback
• Released: 21.01.2008
• EAN: 9780521055215
• ISBN: 978-0-521-05521-5
• No. of pages: 372
• Series: Cambridge Tracts in Mathematic
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Geometry