| Algebraic L-Theory and Topological Manifolds Contributor(s): Ranicki, Andrew (Author), Ranicki, A. a. (Author), Bollobas, Bela (Editor) |
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ISBN: 0521420245 ISBN-13: 9780521420242 Publisher: Cambridge University Press OUR PRICE: $152.00 Product Type: Hardcover - Other Formats Published: January 1993 Annotation: 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 Poincare 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 Poincare 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - General - Mathematics | Applied - Mathematics | Topology - General |
| Dewey: 514.72 |
| LCCN: 92006785 |
| Series: Lezioni Lincee |
| Physical Information: 1.25" H x 6.42" W x 9.26" (1.65 lbs) 372 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 Poincar 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 Poincar 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. |