Other available formats:
Looking for an examination copy?
This title is not currently available for examination. However, if you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact email@example.com providing details of the course you are teaching.
This book presents the definitive account of the applications of this algebra 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.
Reviews & endorsements
"...develops lower K- and L-theory with a view to applications in topology....Apart from the obvious interest of this text both to topologists and to K-theorists, it also serves as an introduction to the field, since there is a comprehensive survey of previous results and applications." M.E. Keating, Bulletin of the London Mathematical Society
Not yet reviewed
Be the first to review
Review was not posted due to profanity×
- Date Published: January 2008
- format: Paperback
- isbn: 9780521055215
- length: 372 pages
- dimensions: 228 x 151 x 20 mm
- weight: 0.6kg
- availability: Available
Table of Contents
Part I. Algebra:
1. Algebraic Poincaré complexes
2. Algebraic normal complexes
3. Algebraic bordism categories
4. Categories over complexes
6. Simply connected assembly
7. Derived product and Hom
8. Local Poincaré duality
9. Universal assembly
10. The algebraic π-π theorem
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
22. Finite fundamental group
24. Higher signatures
25. The 4-periodic theory
26. Surgery with coefficients
Find resources associated with this titleYour search for '' returned .
Type Name Unlocked * Format Size
This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to instructors whose faculty status has been verified. To gain access to locked resources, instructors should sign in to or register for a Cambridge user account.
Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other instructors may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.
Supplementary resources are subject to copyright. Instructors are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.
If you are having problems accessing these resources please contact firstname.lastname@example.org.
Sorry, this resource is locked
Are you sure you want to delete your account?
This cannot be undone.
Thank you for your feedback which will help us improve our service.
If you requested a response, we will make sure to get back to you shortly.×