Algebraic L-theory and Topological Manifolds - A. A. Ranicki

Algebraic L-theory and Topological Manifolds

(Autor)

Buch | Softcover
372 Seiten
2008
Cambridge University Press (Verlag)
978-0-521-05521-5 (ISBN)
64,80 inkl. MwSt
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. The difference between the homotopy types of manifolds and Poincaré 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.

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 π-π 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.

Erscheint lt. Verlag 21.1.2008
Reihe/Serie Cambridge Tracts in Mathematics
Zusatzinfo Worked examples or Exercises
Verlagsort Cambridge
Sprache englisch
Maße 151 x 228 mm
Gewicht 600 g
Themenwelt Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 0-521-05521-0 / 0521055210
ISBN-13 978-0-521-05521-5 / 9780521055215
Zustand Neuware
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