Articles liés à Algebraic L-theory and Topological Manifolds

Algebraic L-theory and Topological Manifolds - Couverture rigide

Ranicki, A. A.

 
9780521420242: Algebraic L-theory and Topological Manifolds
Couverture rigide
ISBN 10 : 0521420245 ISBN 13 : 9780521420242
Editeur : Cambridge University Press, 1992

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Revue de presse

"...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

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Cambridge University Press
Date d'édition
1992
Langue
anglais
ISBN 10 
0521420245
ISBN 13 
9780521420242
Reliure
Relié
Nombre de pages
372
Coordonnées du fabricant
non disponible
Personne responsable
Avery
https://www.avery.fr/

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Dardilly
France