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Lezioni Lincee #102: Algebraic _L-Theory and Topological Manifolds

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Lezioni Lincee #102: Algebraic _L-Theory and Topological Manifolds Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

Surgery theory is the main technique for classifying high-dimensional topological manifolds. Algebraic L-theory is the name of the abstract algebra used to study their geometric properties; it involves the study of quadratic forms. Assuming no previous acquaintance with surgery theory and justifying all the algebraic concepts used by their relevance to topology, Dr Ranicki explains the applications of quadratic forms to the classification of topological manifolds, in a unified algebraic framework.

Synopsis:

on of topological manifolds, in a unified algebraic framework.

Synopsis:

This book explains the applications of quadratic forms to the classification of topological manifolds, in a unified algebraic framework.

Table of Contents

Introduction; Part I. Algebra: 1. Algebraic Poincarécomplexes; 2. Algebraic normal complexes; 3. Algebraic normal categories; 4. Categories over complexes; 5. Duality; 6. Simply-connected assembly; 7. Derived products and Hom; 8. Local Poincaréduality; 9. Universal assembly; 10. The algebraic -theorem; 11. ­-sets; 12. Generalised 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 Poincarécomplexes; 20. The simply-connected case; 21. Transfer; 22. Finite fundamental group; 23. Splitting; 24. Higher signatures; 25. Periodicity; 26. Surgery with coefficients; Appendices; References; Index.

Product Details

ISBN:
9780521420242
Author:
Ranicki, Andrew
Publisher:
Cambridge University Press
Editor:
Bollobas, Bela
Editor:
Bollobas, B.
Author:
Kirwan, F.
Author:
Ranicki, A. A.
Author:
Katok, A.
Author:
Bollobas, B.
Author:
Fulton, W.
Author:
Sarnak, P.
Location:
Cambridge England ;
Subject:
Surgery
Subject:
Applied
Subject:
Geometry - General
Subject:
Forms, quadratic
Subject:
Topological manifolds
Subject:
Surgery (Topology)
Subject:
Complexes, Cochain.
Subject:
Cochain complexes.
Subject:
Surgery (Topology) Surgery (Topology)
Subject:
Topology - General
Subject:
Mathematics-Geometry and Trigonometry
Series:
Lezioni Lincee
Series Volume:
102
Publication Date:
20030231
Binding:
Hardcover
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
Yes
Pages:
372
Dimensions:
9.26x6.42x1.25 in. 1.65 lbs.

Related Subjects

History and Social Science » World History » General
Science and Mathematics » Environmental Studies » General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » Topology
Science and Mathematics » Physics » General

Lezioni Lincee #102: Algebraic _L-Theory and Topological Manifolds New Hardcover
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$193.25 In Stock
Product details 372 pages Cambridge University Press - English 9780521420242 Reviews:
"Synopsis" by , Surgery theory is the main technique for classifying high-dimensional topological manifolds. Algebraic L-theory is the name of the abstract algebra used to study their geometric properties; it involves the study of quadratic forms. Assuming no previous acquaintance with surgery theory and justifying all the algebraic concepts used by their relevance to topology, Dr Ranicki explains the applications of quadratic forms to the classification of topological manifolds, in a unified algebraic framework.
"Synopsis" by , on of topological manifolds, in a unified algebraic framework.
"Synopsis" by , This book explains the applications of quadratic forms to the classification of topological manifolds, in a unified algebraic framework.
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