Stable Modules and the D(2)-Problem

F. E. A. Johnson

ISBN 10: 0521537495 / ISBN 13: 9780521537490

Edité par Cambridge University Press, 2003

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - This 2003 book is concerned with two fundamental problems in low-dimensional topology. Firstly, the D(2)-problem, which asks whether cohomology detects dimension, and secondly the realization problem, which asks whether every algebraic 2-complex is geometrically realizable. The author shows that for a large class of fundamental groups these problems are equivalent. Moreover, in the case of finite groups, Professor Johnson develops general methods and gives complete solutions in a number of cases. In particular, he presents a complete treatment of Yoneda extension theory from the viewpoint of derived objects and proves that for groups of period four, two-dimensional homotopy types are parametrized by isomorphism classes of projective modules. This book is carefully written with an eye on the wider context and as such is suitable for graduate students wanting to learn low-dimensional homotopy theory as well as established researchers in the field.

N° de réf. du vendeur 9780521537490

Détails bibliographiques

• Titre: Stable Modules and the D(2)-Problem
• Éditeur: Cambridge University Press
• Date de parution: 2003
• Langue: anglais
• ISBN à 10 chiffres: 0521537495
• ISBN à 13 chiffres: 9780521537490
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 229 L x 152 H x 17 P (en millimètres) 229 millimètres de largeur par 152 millimètres de hauteur par 17 millimètres de profondeur
• Poids: 459 grammes

A propos de ce titre

Synopsis

This 2003 book deals with two fundamental problems in low-dimensional topology with an eye on wider context.

Présentation de l'éditeur

This 2003 book is concerned with two fundamental problems in low-dimensional topology. Firstly, the D(2)-problem, which asks whether cohomology detects dimension, and secondly the realization problem, which asks whether every algebraic 2-complex is geometrically realizable. The author shows that for a large class of fundamental groups these problems are equivalent. Moreover, in the case of finite groups, Professor Johnson develops general methods and gives complete solutions in a number of cases. In particular, he presents a complete treatment of Yoneda extension theory from the viewpoint of derived objects and proves that for groups of period four, two-dimensional homotopy types are parametrized by isomorphism classes of projective modules. This book is carefully written with an eye on the wider context and as such is suitable for graduate students wanting to learn low-dimensional homotopy theory as well as established researchers in the field.