Algebraic L-theory and Topological Manifolds
Part of Cambridge Tracts in Mathematics
- Author: A. A. Ranicki, University of Edinburgh
- Date Published: March 2008
- availability: Available
- format: Paperback
- isbn: 9780521055215
Paperback
Other available formats:
Hardback
Looking for an inspection copy?
This title is not currently available on inspection
-
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.
Customer reviews
Not yet reviewed
Be the first to review
Review was not posted due to profanity
×Product details
- Date Published: March 2008
- format: Paperback
- isbn: 9780521055215
- length: 372 pages
- dimensions: 228 x 151 x 20 mm
- weight: 0.6kg
- availability: Available
Table of Contents
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.-
General Resources
Find resources associated with this title
Type Name Unlocked * Format Size Showing of
This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to lecturers whose faculty status has been verified. To gain access to locked resources, lecturers 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 lecturers 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. Lecturers 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 lecturers@cambridge.org.
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org
Register Sign in» Proceed
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.
Continue ×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.
×